diff --git a/CHANGES b/CHANGES
--- a/CHANGES
+++ b/CHANGES
@@ -1,3 +1,7 @@
+* 0.3.2: 30 August 2013
+
+  - new Group instance for Endomorphism
+
 * 0.3.1: 20 August 2013
 
   - new module Data.Monoid.Endomorphism
diff --git a/monoid-extras.cabal b/monoid-extras.cabal
--- a/monoid-extras.cabal
+++ b/monoid-extras.cabal
@@ -1,5 +1,5 @@
 name:                monoid-extras
-version:             0.3.1.0
+version:             0.3.2.0
 synopsis:            Various extra monoid-related definitions and utilities
 description:         Various extra monoid-related definitions and utilities,
                      such as monoid actions, monoid coproducts, \"deletable\"
@@ -32,6 +32,8 @@
                      Data.Monoid.WithSemigroup
 
   build-depends:     base >= 4.3 && < 4.8,
+                     groups < 0.4,
+                     groupoids < 4,
                      semigroups >= 0.8 && < 0.10,
                      semigroupoids < 4
 
diff --git a/src/Data/Monoid/Endomorphism.hs b/src/Data/Monoid/Endomorphism.hs
--- a/src/Data/Monoid/Endomorphism.hs
+++ b/src/Data/Monoid/Endomorphism.hs
@@ -15,6 +15,8 @@
     where
 
 import           Control.Category
+import           Data.Group
+import           Data.Groupoid
 import           Data.Semigroup
 import           Data.Semigroupoid
 import           Prelude           hiding (id, (.))
@@ -31,3 +33,6 @@
 instance Category k => Monoid (Endomorphism k a) where
   mempty = Endomorphism id
   Endomorphism a `mappend` Endomorphism b = Endomorphism (a . b)
+
+instance (Category k, Groupoid k) => Group (Endomorphism k a) where
+  invert (Endomorphism a) = Endomorphism (inv a)