diff --git a/include/ceres/ordered_groups.h b/include/ceres/ordered_groups.h
index 9ae8499..6ca82af 100644
--- a/include/ceres/ordered_groups.h
+++ b/include/ceres/ordered_groups.h
@@ -182,7 +182,9 @@
     return group_to_elements_;
   }
 
-  const std::map<T, int>& element_to_group() const { return element_to_group_; }
+  const std::unordered_map<T, int>& element_to_group() const {
+    return element_to_group_;
+  }
 
  private:
   std::map<int, std::set<T>> group_to_elements_;
diff --git a/internal/ceres/reorder_program.cc b/internal/ceres/reorder_program.cc
index fdf8119..e02af43 100644
--- a/internal/ceres/reorder_program.cc
+++ b/internal/ceres/reorder_program.cc
@@ -36,6 +36,7 @@
 #include <numeric>
 #include <set>
 #include <string>
+#include <unordered_map>
 #include <vector>
 
 #include "Eigen/SparseCore"
@@ -228,28 +229,49 @@
     return false;
   }
 
-  std::vector<ParameterBlock*>* parameter_blocks =
-      program->mutable_parameter_blocks();
-  parameter_blocks->clear();
+  const std::unordered_map<double*, int>& element_to_group =
+      ordering.element_to_group();
 
-  // TODO(sameeragarwal): Investigate whether this should be a set or an
-  // unordered_set.
-  const std::map<int, std::set<double*>>& groups = ordering.group_to_elements();
-  for (const auto& p : groups) {
-    const std::set<double*>& group = p.second;
-    for (double* parameter_block_ptr : group) {
-      auto it = parameter_map.find(parameter_block_ptr);
-      if (it == parameter_map.end()) {
-        *error = absl::StrFormat(
-            "User specified ordering contains a pointer "
-            "to a double that is not a parameter block in "
-            "the problem. The invalid double is in group: %d",
-            p.first);
-        return false;
-      }
-      parameter_blocks->push_back(it->second);
+  // Check that all the elements in the ordering are in the problem.
+  for (const auto& p : element_to_group) {
+    auto it = parameter_map.find(p.first);
+    if (it == parameter_map.end()) {
+      *error = absl::StrFormat(
+          "User specified ordering contains a pointer "
+          "to a double that is not a parameter block in "
+          "the problem. The invalid double is in group: %d",
+          p.second);
+      return false;
     }
   }
+
+  // Add the parameter blocks to the new ordering, while maintaining the
+  // original ordering of the parameter blocks within each group.
+  const std::vector<ParameterBlock*> old_parameter_blocks =
+      program->parameter_blocks();
+  std::vector<ParameterBlock*>* parameter_blocks =
+      program->mutable_parameter_blocks();
+  const std::map<int, std::set<double*>>& group_to_elements =
+      ordering.group_to_elements();
+  std::map<int, int> group_to_index;
+  int group_cursor = 0;
+  for (const auto& p : group_to_elements) {
+    group_to_index[p.first] = group_cursor;
+    group_cursor += p.second.size();
+  }
+  for (ParameterBlock* block : old_parameter_blocks) {
+    const auto it = element_to_group.find(block->mutable_user_state());
+    if (it == element_to_group.end()) {
+      *error = absl::StrFormat("No ordering specified for parameter block: %d",
+                               block->index());
+      return false;
+    }
+    const int group = it->second;
+    int& index = group_to_index[group];
+    (*parameter_blocks)[index] = block;
+    index++;
+  }
+
   return true;
 }
 
diff --git a/internal/ceres/reorder_program_test.cc b/internal/ceres/reorder_program_test.cc
index 0e1fa05..a2cbeb3 100644
--- a/internal/ceres/reorder_program_test.cc
+++ b/internal/ceres/reorder_program_test.cc
@@ -171,6 +171,73 @@
   EXPECT_EQ(parameter_blocks[2]->user_state(), &y);
 }
 
+// Test that ApplyOrdering preserves the original program order within each
+// group. This is essential for deterministic behavior - without preserving
+// the original order, the ordering would depend on pointer addresses which
+// can vary between runs due to ASLR or different memory allocation patterns.
+TEST(_, ApplyOrderingPreservesOrderWithinGroups) {
+  // Use heap-allocated parameter blocks to ensure pointer addresses are
+  // not in any predictable order (simulating what happens in real usage).
+  std::vector<std::unique_ptr<double[]>> params;
+  std::vector<double*> param_ptrs;
+  const int kNumParams = 10;
+
+  for (int i = 0; i < kNumParams; ++i) {
+    params.push_back(std::make_unique<double[]>(3));
+    param_ptrs.push_back(params.back().get());
+  }
+
+  // Shuffle the parameter pointers to generate non-deterministic addresses
+  // in case the allocator happens to return addresses in a specific order.
+  // We add them to the problem in a specific order, which
+  // should be preserved within each group after ApplyOrdering.
+  std::mt19937 rng(42);  // Fixed seed for reproducibility
+  std::shuffle(param_ptrs.begin(), param_ptrs.end(), rng);
+
+  ProblemImpl problem;
+
+  // Add parameter blocks in the order of their index (0, 1, 2, ..., 9)
+  // but use the original param_ptrs which may have any address ordering.
+  for (int i = 0; i < kNumParams; ++i) {
+    problem.AddParameterBlock(param_ptrs[i], 3);
+  }
+
+  // Assign parameters to groups:
+  // Group 0: params 0, 2, 4, 6, 8 (evens)
+  // Group 1: params 1, 3, 5, 7, 9 (odds)
+  ParameterBlockOrdering linear_solver_ordering;
+  for (int i = 0; i < kNumParams; ++i) {
+    linear_solver_ordering.AddElementToGroup(param_ptrs[i], i % 2);
+  }
+
+  Program* program = problem.mutable_program();
+  std::string message;
+
+  EXPECT_TRUE(ApplyOrdering(
+      problem.parameter_map(), linear_solver_ordering, program, &message));
+
+  const std::vector<ParameterBlock*>& parameter_blocks =
+      program->parameter_blocks();
+
+  EXPECT_EQ(parameter_blocks.size(), kNumParams);
+
+  // Check that group 0 elements (evens) come first and
+  // maintain their original relative order.
+  EXPECT_EQ(parameter_blocks[0]->user_state(), param_ptrs[0]);
+  EXPECT_EQ(parameter_blocks[1]->user_state(), param_ptrs[2]);
+  EXPECT_EQ(parameter_blocks[2]->user_state(), param_ptrs[4]);
+  EXPECT_EQ(parameter_blocks[3]->user_state(), param_ptrs[6]);
+  EXPECT_EQ(parameter_blocks[4]->user_state(), param_ptrs[8]);
+
+  // Check that group 1 elements (odds) come second and
+  // maintain their original relative order.
+  EXPECT_EQ(parameter_blocks[5]->user_state(), param_ptrs[1]);
+  EXPECT_EQ(parameter_blocks[6]->user_state(), param_ptrs[3]);
+  EXPECT_EQ(parameter_blocks[7]->user_state(), param_ptrs[5]);
+  EXPECT_EQ(parameter_blocks[8]->user_state(), param_ptrs[7]);
+  EXPECT_EQ(parameter_blocks[9]->user_state(), param_ptrs[9]);
+}
+
 #ifndef CERES_NO_SUITESPARSE
 class ReorderProgramForSparseCholeskyUsingSuiteSparseTest
     : public ::testing::Test {