diff --git a/src/rigid.cpp b/src/rigid.cpp
index f3357dbf..36fe8b48 100644
--- a/src/rigid.cpp
+++ b/src/rigid.cpp
@@ -75,8 +75,9 @@ void Rigid::denormalize(const Normalization& normalization,
     result.translation =
         normalization.scale * result.translation + normalization.fixed_mean -
         result.scale * result.rotation * normalization.moving_mean;
-    result.points = result.points * normalization.scale +
-                    normalization.fixed_mean.replicate(result.points.rows(), 1);
+    result.points =
+        result.points * normalization.scale +
+        normalization.fixed_mean.transpose().replicate(result.points.rows(), 1);
 }
 
 Rigid::Result rigid(const Matrix& fixed, const Matrix& moving) {
diff --git a/test/rigid.cpp b/test/rigid.cpp
index b4ff286b..9aaeed1c 100644
--- a/test/rigid.cpp
+++ b/test/rigid.cpp
@@ -93,6 +93,7 @@ TEST_F(Rigid2DTest, Normalize) {
     m_fish_transformed = m_fish * rotation;
     auto result = rigid(m_fish_transformed, m_fish);
     EXPECT_TRUE(result.rotation.isApprox(rotation.transpose(), TOLERANCE));
+    EXPECT_EQ(result.points.rows(), m_fish.rows());
 }
 
 TEST_P(Rotation2D, IsRecovered) {