diff --git a/homeassistant/components/integration/sensor.py b/homeassistant/components/integration/sensor.py
index 40229404288..8cf5da5bc7c 100644
--- a/homeassistant/components/integration/sensor.py
+++ b/homeassistant/components/integration/sensor.py
@@ -196,10 +196,11 @@ class IntegrationSensor(RestoreEntity, SensorEntity):
             # or device_class.
             update_state = False
 
-            if self._unit_of_measurement is None:
-                unit = new_state.attributes.get(ATTR_UNIT_OF_MEASUREMENT)
-                if unit is not None:
-                    self._unit_of_measurement = self._unit_template.format(unit)
+            unit = new_state.attributes.get(ATTR_UNIT_OF_MEASUREMENT)
+            if unit is not None:
+                new_unit_of_measurement = self._unit_template.format(unit)
+                if self._unit_of_measurement != new_unit_of_measurement:
+                    self._unit_of_measurement = new_unit_of_measurement
                     update_state = True
 
             if (