diff --git a/cython/gtsam/tests/test_KarcherMeanFactor.py b/cython/gtsam/tests/test_KarcherMeanFactor.py
new file mode 100644
index 000000000..6976decc1
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+++ b/cython/gtsam/tests/test_KarcherMeanFactor.py
@@ -0,0 +1,80 @@
+"""
+GTSAM Copyright 2010-2019, Georgia Tech Research Corporation,
+Atlanta, Georgia 30332-0415
+All Rights Reserved
+
+See LICENSE for the license information
+
+KarcherMeanFactor unit tests.
+Author: Frank Dellaert
+"""
+
+# pylint: disable=invalid-name, no-name-in-module, no-member
+
+import unittest
+
+import gtsam
+import numpy as np
+from gtsam.utils.test_case import GtsamTestCase
+
+KEY = 0
+MODEL = gtsam.noiseModel_Unit.Create(3)
+
+
+def find_Karcher_mean_Rot3(rotations):
+    """Find the Karcher mean of given values."""
+    # Cost function C(R) = \sum PriorFactor(R_i)::error(R)
+    # No closed form solution.
+    graph = gtsam.NonlinearFactorGraph()
+    for R in rotations:
+        graph.add(gtsam.PriorFactorRot3(KEY, R, MODEL))
+    initial = gtsam.Values()
+    initial.insert(KEY, gtsam.Rot3())
+    result = gtsam.GaussNewtonOptimizer(graph, initial).optimize()
+    return result.atRot3(KEY)
+
+
+# Rot3 version
+R = gtsam.Rot3.Expmap(np.array([0.1, 0, 0]))
+
+
+class TestKarcherMean(GtsamTestCase):
+
+    def test_find(self):
+        # Check that optimizing for Karcher mean (which minimizes Between distance)
+        # gets correct result.
+        rotations = {R, R.inverse()}
+        expected = gtsam.Rot3()
+        actual = find_Karcher_mean_Rot3(rotations)
+        self.gtsamAssertEquals(expected, actual)
+
+    def test_factor(self):
+        """Check that the InnerConstraint factor leaves the mean unchanged."""
+        # Make a graph with two variables, one between, and one InnerConstraint
+        # The optimal result should satisfy the between, while moving the other
+        # variable to make the mean the same as before.
+        # Mean of R and R' is identity. Let's make a BetweenFactor making R21 =
+        # R*R*R, i.e. geodesic length is 3 rather than 2.
+        graph = gtsam.NonlinearFactorGraph()
+        R12 = R.compose(R.compose(R))
+        graph.add(gtsam.BetweenFactorRot3(1, 2, R12, MODEL))
+        keys = gtsam.KeyVector()
+        keys.push_back(1)
+        keys.push_back(2)
+        graph.add(gtsam.KarcherMeanFactorRot3(keys))
+
+        initial = gtsam.Values()
+        initial.insert(1, R.inverse())
+        initial.insert(2, R)
+        expected = find_Karcher_mean_Rot3([R, R.inverse()])
+
+        result = gtsam.GaussNewtonOptimizer(graph, initial).optimize()
+        actual = find_Karcher_mean_Rot3(
+            [result.atRot3(1), result.atRot3(2)])
+        self.gtsamAssertEquals(expected, actual)
+        self.gtsamAssertEquals(
+            R12, result.atRot3(1).between(result.atRot3(2)))
+
+
+if __name__ == "__main__":
+    unittest.main()