diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index 2101d802264c..c98f7082907f 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -1584,18 +1584,12 @@ def set_units(self, u):
         ----------
         u : units tag
         """
-        pchanged = False
-        if u is None:
-            self.units = None
-            pchanged = True
-        else:
-            if u != self.units:
-                self.units = u
-                pchanged = True
-        if pchanged:
-            self._update_axisinfo()
-            self.callbacks.process('units')
-            self.callbacks.process('units finalize')
+        if u == self.units:
+            return
+        self.units = u
+        self._update_axisinfo()
+        self.callbacks.process('units')
+        self.callbacks.process('units finalize')
         self.stale = True
 
     def get_units(self):