diff --git a/tensorflow/lite/experimental/ruy/BUILD b/tensorflow/lite/experimental/ruy/BUILD
index 46fbf3cf3ce..29061e1782f 100644
--- a/tensorflow/lite/experimental/ruy/BUILD
+++ b/tensorflow/lite/experimental/ruy/BUILD
@@ -207,6 +207,7 @@ cc_test(
         ":block_map",
         ":cpu_cache_size",
         ":path",
+        ":side_pair",
         "@com_google_googletest//:gtest",
     ],
 )
diff --git a/tensorflow/lite/experimental/ruy/block_map_test.cc b/tensorflow/lite/experimental/ruy/block_map_test.cc
index 54b32e46a6c..fd322ab66ca 100644
--- a/tensorflow/lite/experimental/ruy/block_map_test.cc
+++ b/tensorflow/lite/experimental/ruy/block_map_test.cc
@@ -17,11 +17,14 @@ limitations under the License.
 
 #include <cstddef>
 #include <cstdint>
+#include <cstdlib>
 #include <limits>
+#include <vector>
 
 #include <gtest/gtest.h>
 #include "tensorflow/lite/experimental/ruy/cpu_cache_size.h"
 #include "tensorflow/lite/experimental/ruy/path.h"
+#include "tensorflow/lite/experimental/ruy/side_pair.h"
 
 namespace ruy {
 namespace {
@@ -142,6 +145,115 @@ TEST(BlockMapTest, MakeBlockMapTuningTestRectangular) {
 
 #endif
 
+int L1Distance(const SidePair<int>& a, const SidePair<int>& b) {
+  return std::abs(a[Side::kLhs] - b[Side::kLhs]) +
+         std::abs(a[Side::kRhs] - b[Side::kRhs]);
+}
+
+void GetBlockByIndexSquareTest(int num_blocks_base_log2,
+                               BlockMapTraversalOrder traversal_order) {
+  // Arbitrary, does not affect this test. 3 is just a typical value.
+  constexpr int kKernelSizeLog2 = 3;
+
+  const int size_log2 = num_blocks_base_log2 + kKernelSizeLog2;
+  BlockMap block_map;
+  block_map.thread_count = 1;
+  block_map.traversal_order = traversal_order;
+  block_map.num_blocks_base_log2 = num_blocks_base_log2;
+  for (Side side : {Side::kLhs, Side::kRhs}) {
+    block_map.dims[side] = 1 << size_log2;
+    block_map.rectangularness_log2[side] = 0;
+    block_map.kernel_dims[side] = 1 << kKernelSizeLog2;
+    block_map.small_block_dims[side] = block_map.kernel_dims[side];
+    block_map.large_blocks[side] = 0;
+  }
+
+  const int num_blocks_per_side = 1 << num_blocks_base_log2;
+  const int num_blocks = num_blocks_per_side * num_blocks_per_side;
+  EXPECT_EQ(num_blocks, NumBlocks(block_map));
+
+  // Perform a full traversal of all blocks, as if computing a whole matrix
+  // multiplication.
+  //
+  // Used to record how many times each block was hit by the traversal.
+  std::vector<int> block_hit_counts(num_blocks);
+  // Here we guard an assumption that all traversal orders start at (0, 0).
+  SidePair<int> previous_block_coords(0, 0);
+  // Sum of L1 norm of the coordinate change at every step of the traversal.
+  std::int64_t total_l1_distance = 0;
+  // Number of jumps i.e. traversal steps with a L1 norm greater than 1.
+  int discontinuity_count = 0;
+  for (int block_index = 0; block_index < num_blocks; block_index++) {
+    SidePair<int> block_coords;
+    GetBlockByIndex(block_map, block_index, &block_coords);
+    ++block_hit_counts[block_coords[Side::kLhs] +
+                       num_blocks_per_side * block_coords[Side::kRhs]];
+    int distance = L1Distance(block_coords, previous_block_coords);
+    total_l1_distance += distance;
+    discontinuity_count += (distance > 1);
+    previous_block_coords = block_coords;
+  }
+
+  // Verify that each block was traversed exactly once.
+  for (int l = 0; l < num_blocks_per_side; l++) {
+    for (int r = 0; r < num_blocks_per_side; r++) {
+      EXPECT_EQ(block_hit_counts[l + num_blocks_per_side * r], 1);
+    }
+  }
+
+  // Verify that the discontinuity_count and total_l1_distance are as expected
+  // for the given traversal_order.
+  switch (traversal_order) {
+    case BlockMapTraversalOrder::kFractalHilbert:
+      // No discontinuity at all with this space-filling continuous curve!
+      EXPECT_EQ(discontinuity_count, 0);
+      // Therefore, total_l1_distance has to be the number of blocks minus one.
+      EXPECT_EQ(total_l1_distance, num_blocks - 1);
+      break;
+    case BlockMapTraversalOrder::kLinear:
+      EXPECT_EQ(discontinuity_count, num_blocks_per_side - 1);
+      EXPECT_EQ(total_l1_distance,
+                2 * num_blocks_per_side * (num_blocks_per_side - 1));
+      break;
+    case BlockMapTraversalOrder::kFractalZ:
+      EXPECT_EQ(discontinuity_count, num_blocks > 1 ? (num_blocks / 2 - 1) : 0);
+      EXPECT_EQ(total_l1_distance,
+                2 * num_blocks_per_side * (num_blocks_per_side - 1));
+      break;
+    case BlockMapTraversalOrder::kFractalU: {
+      if (num_blocks_base_log2 == 0) {
+        EXPECT_EQ(discontinuity_count, 0);
+        EXPECT_EQ(total_l1_distance, 0);
+      } else {
+        int expected_discontinuity_count = 0;
+        int expected_total_l1_distance = 3;
+        for (int i = 2; i <= num_blocks_base_log2; i++) {
+          expected_discontinuity_count = 4 * expected_discontinuity_count + 2;
+          expected_total_l1_distance =
+              4 * expected_total_l1_distance + (1 << (i + 1)) - 1;
+        }
+        EXPECT_EQ(discontinuity_count, expected_discontinuity_count);
+        EXPECT_EQ(total_l1_distance, expected_total_l1_distance);
+      }
+      break;
+    }
+    default:
+      abort();
+  }
+}
+
+TEST(BlockMapTest, GetBlockByIndexSquare) {
+  for (int num_blocks_base_log2 = 0; num_blocks_base_log2 <= 10;
+       num_blocks_base_log2++) {
+    for (BlockMapTraversalOrder traversal_order :
+         {BlockMapTraversalOrder::kLinear, BlockMapTraversalOrder::kFractalZ,
+          BlockMapTraversalOrder::kFractalU,
+          BlockMapTraversalOrder::kFractalHilbert}) {
+      GetBlockByIndexSquareTest(num_blocks_base_log2, traversal_order);
+    }
+  }
+}
+
 }  // namespace
 }  // namespace ruy