diff --git a/pointmatcher/TransformationsImpl.cpp b/pointmatcher/TransformationsImpl.cpp
index 36da5a02..562f063f 100644
--- a/pointmatcher/TransformationsImpl.cpp
+++ b/pointmatcher/TransformationsImpl.cpp
@@ -125,8 +125,14 @@ typename PointMatcher<T>::TransformationParameters TransformationsImpl<T>::Rigid
 	}
 	else if(ortho.cols() == 3)
 	{
+		const T epsilon = 0.001;
+
 		// R = [ a b]
 		//     [-b a]
+		if(anyabs(parameters(0,0) - parameters(1,1)) > epsilon || anyabs(parameters(1,0) + parameters(0,1)) > epsilon)
+		{
+			throw TransformationError("RigidTransformation: Error, only proper rigid transformations are supported.");
+		}
 		
 		// mean of a and b
 		T a = (parameters(0,0) + parameters(1,1))/2; 	
diff --git a/utest/ui/Transformations.cpp b/utest/ui/Transformations.cpp
index 23a887e4..918b5533 100644
--- a/utest/ui/Transformations.cpp
+++ b/utest/ui/Transformations.cpp
@@ -103,20 +103,29 @@ TEST(Transformation, RigidTransformation)
 
 	//-------------------------------------
 	// Construct a 2D non-orthogonal matrix
-	PM::Matrix T_2D = PM::Matrix::Identity(3,3);
-	T_2D(1,0) = 8.99;
-	T_2D(0,1) = 4.03;
+	PM::Matrix T_2D_non_ortho = PM::Matrix::Identity(3,3);
+	T_2D_non_ortho(0,0) = 0.8;
+	T_2D_non_ortho(0,1) = -0.5;
+	T_2D_non_ortho(1,0) = 0.5;
+	T_2D_non_ortho(1,1) = 0.8;
 
-	EXPECT_FALSE(rigidTrans->checkParameters(T_2D));
+	EXPECT_FALSE(rigidTrans->checkParameters(T_2D_non_ortho));
 
-	EXPECT_THROW(rigidTrans->compute(data2D, T_2D), TransformationError);
+	EXPECT_THROW(rigidTrans->compute(data2D, T_2D_non_ortho), TransformationError);
 
 	// Check stability over iterations
 	for(int i = 0; i < 10; i++)
 	{
-		T_2D = rigidTrans->correctParameters(T_2D);
-		EXPECT_TRUE(rigidTrans->checkParameters(T_2D));
+		T_2D_non_ortho = rigidTrans->correctParameters(T_2D_non_ortho);
+		EXPECT_TRUE(rigidTrans->checkParameters(T_2D_non_ortho));
 	}
 
+	//-------------------------------------
+	// Construct a 2D reflection matrix
+	PM::Matrix T_2D_reflection = PM::Matrix::Identity(3,3);
+	T_2D_reflection(1,1) = -1;
+
+	EXPECT_THROW(rigidTrans->correctParameters(T_2D_reflection), TransformationError);
+
 	delete rigidTrans;
 }