diff --git a/tests/test_secondary_rvs.py b/tests/test_secondary_rvs.py
index 8b2ef9ab..f5064734 100644
--- a/tests/test_secondary_rvs.py
+++ b/tests/test_secondary_rvs.py
@@ -4,7 +4,7 @@
 from pandas import DataFrame
 
 from orbitize.kepler import calc_orbit
-from orbitize import read_input, system, sampler
+from orbitize import read_input, system, sampler, DATADIR
 
 
 def test_secondary_rv_lnlike_calc():
@@ -64,6 +64,16 @@ def test_secondary_rv_lnlike_calc():
 
     assert np.all(rv0 == -m1 / m0 * rv1)
 
+def test_read_input():
+    """
+    Test that reading in a data file with only a companion RV and relative astrometry
+    works. Added in response to issue #351.
+    """
+
+    input_data = read_input.read_file('{}/HD4747.csv'.format(DATADIR)) 
+    input_data['object'] = 1 # make sure all astrometry and RV is marked as of the secondary
+    mySystem = system.System(1, input_data, 1, 1, fit_secondary_mass=False)
 
 if __name__ == "__main__":
-    test_secondary_rv_lnlike_calc()
+    # test_secondary_rv_lnlike_calc()
+    test_read_input()