diff --git a/tests/data/test_cf_units.py b/tests/data/test_cf_units.py
index ba008bbec4a5aea31457587614dd6899245d5d11..a7fbd7c02b04c845b51414c6106c6fce0af7bf81 100644
--- a/tests/data/test_cf_units.py
+++ b/tests/data/test_cf_units.py
@@ -23,9 +23,9 @@ class TestCfUnits(unittest.TestCase):
         self.assertEqual(u("degC"), "°C")
         self.assertEqual(u("degree_Celsius"), "°C")
 
-        self.assertEqual(u(""), "dimensionless")
-        self.assertEqual(u("1"), "dimensionless")
-        self.assertEqual(u("m/m"), "dimensionless")
+        self.assertEqual(u(""), "")
+        self.assertEqual(u("1"), "")
+        self.assertEqual(u("m/m"), "")
 
         self.assertEqual(u("m/s"), "m s-1")
         self.assertEqual(u("m s-1"), "m s-1")