diff --git a/gtsam/linear/tests/testNoiseModel.cpp b/gtsam/linear/tests/testNoiseModel.cpp
index 6b130bea0..f8ce1feca 100644
--- a/gtsam/linear/tests/testNoiseModel.cpp
+++ b/gtsam/linear/tests/testNoiseModel.cpp
@@ -452,19 +452,24 @@ TEST(NoiseModel, WhitenInPlace)
 /*
  * These tests are responsible for testing the weight functions for the m-estimators in GTSAM.
  * The weight function is related to the analytic derivative of the residual function. See
- *  http://research.microsoft.com/en-us/um/people/zhang/INRIA/Publis/Tutorial-Estim/node24.html
+ *  https://members.loria.fr/MOBerger/Enseignement/Master2/Documents/ZhangIVC-97-01.pdf
  * for details. This weight function is required when optimizing cost functions with robust
  * penalties using iteratively re-weighted least squares.
  */
 
 TEST(NoiseModel, robustFunctionHuber)
 {
-  const double k = 5.0, error1 = 1.0, error2 = 10.0;
+  const double k = 5.0, error1 = 1.0, error2 = 10.0, error3 = -10.0, error4 = -1.0;
   const mEstimator::Huber::shared_ptr huber = mEstimator::Huber::Create(k);
   const double weight1 = huber->weight(error1),
-               weight2 = huber->weight(error2);
+               weight2 = huber->weight(error2),
+               weight3 = huber->weight(error3),
+               weight4 = huber->weight(error4);
   DOUBLES_EQUAL(1.0, weight1, 1e-8);
   DOUBLES_EQUAL(0.5, weight2, 1e-8);
+  // Test negative value to ensure we take absolute value of error.
+  DOUBLES_EQUAL(0.5, weight3, 1e-8);
+  DOUBLES_EQUAL(1.0, weight4, 1e-8);
 }
 
 TEST(NoiseModel, robustFunctionGemanMcClure)