diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,9 @@
 # Revision history for monadic-recursion-schemes
 
+## 0.1.4.1 -- 2020-05-14
+
+* add alternative for dynaM and codynaM
+
 ## 0.1.4.0 -- 2020-05-14
 
 * add dynaM, codynaM and dynaM' the recursive variant.
diff --git a/monadic-recursion-schemes.cabal b/monadic-recursion-schemes.cabal
--- a/monadic-recursion-schemes.cabal
+++ b/monadic-recursion-schemes.cabal
@@ -4,7 +4,7 @@
 -- http://haskell.org/cabal/users-guide/
 
 name:                monadic-recursion-schemes
-version:             0.1.4.0
+version:             0.1.4.1
 synopsis:            Recursion Schemes for Monadic version.
 description:         Yet another recursion schemes for monadic style, depends on recursion-schemes.
 homepage:            https://github.com/cutsea110/monadic-recursion-schemes.git
diff --git a/src/Data/Functor/Foldable/Monadic.hs b/src/Data/Functor/Foldable/Monadic.hs
--- a/src/Data/Functor/Foldable/Monadic.hs
+++ b/src/Data/Functor/Foldable/Monadic.hs
@@ -17,7 +17,8 @@
   , chronoM, cochronoM
   , chronoM' -- cochronoM'
   , dynaM, codynaM
-  , dynaM' -- codynaM'
+  , dynaM', codynaM'
+  , dynaM'', codynaM''
   ) where
 
 import           Control.Comonad              (Comonad (..))
@@ -43,7 +44,7 @@
      => (a -> m (Base t a)) -- ^ coalgebra
      -> a -> m t
 anaM psi = h
-  where h = (return . embed) <=< mapM h <=< psi
+  where h = return . embed <=< mapM h <=< psi
 
 -- | paramorphism
 paraM :: (Monad m, Traversable (Base t), Recursive t)
@@ -57,7 +58,7 @@
      => (a -> m (Base t (Either t a))) -- ^ coalgebra
      -> a -> m t
 apoM psi = h
-  where h = (return . embed) <=< mapM (either return h) <=< psi
+  where h = return . embed <=< mapM (either return h) <=< psi
 
 -- | histomorphism on anamorphism variant
 histoM :: (Monad m, Traversable (Base t), Recursive t)
@@ -65,7 +66,7 @@
        -> t -> m a
 histoM phi = h
   where h = phi <=< mapM f . project
-        f = anaM (liftM2 (Cf.:<) <$> h <*> (return . project))
+        f = anaM (liftM2 (Cf.:<) <$> h <*> return . project)
 
 -- | histomorphism on catamorphism variant
 histoM' :: (Monad m, Traversable (Base t), Recursive t)
@@ -79,7 +80,7 @@
       => (a -> m (Base t (Free (Base t) a))) -- ^ coalgebra
       -> a -> m t
 futuM psi = h
-  where h = (return . embed) <=< mapM f <=< psi
+  where h = return . embed <=< mapM f <=< psi
         f = cataM $ \case
           Fr.Pure  a -> h a
           Fr.Free fb -> return (embed fb)
@@ -129,7 +130,7 @@
       -> (s -> m (Base s s)) -- ^ coalgebra
       -> s -> m t
 metaM phi psi = h
-  where h = (return . embed) <=< mapM h . project
+  where h = return . embed <=< mapM h . project
 
 -- | metamorphism on combination variant of cata to ana
 metaM' :: (Monad m, Corecursive c, Traversable (Base c), Traversable (Base t), Recursive t)
@@ -162,24 +163,45 @@
           -> t -> m c
 cochronoM phi psi = futuM psi <=< histoM phi
 
--- | dynamorphism on recursive variant over hylomorphism
-dynaM' :: (Monad m, Traversable t)
-       => (t (Cofree t c) -> m c) -- ^ algebra
-       -> (a -> m (t a))          -- ^ coalgebra
+-- | dynamorphism on recursive variant over chronomorphism
+dynaM :: (Monad m, Traversable (Base t), Recursive t, Corecursive t)
+      => (Base t (Cofree (Base t) b) -> m b) -- ^ algebra
+      -> (a -> m (Base t a))                 -- ^ coalgebra
+      -> a -> m b
+dynaM phi psi = chronoM' phi (return . fmap Pure <=< psi)
+
+-- | dynamorphism on combination variant of ana to histo
+dynaM' :: forall m t a c. (Monad m, Traversable (Base t), Recursive t, Corecursive t)
+       => (Base t (Cofree (Base t) c) -> m c) -- ^ algebra
+       -> (a -> m (Base t a))                 -- ^ coalgebra
        -> a -> m c
-dynaM' phi psi = return . extract <=< hyloM f psi
+dynaM' phi psi = (histoM phi :: t -> m c) <=< (anaM psi :: a -> m t)
+
+-- | dynamorphism on recursive variant over hylomorphism
+dynaM'' :: (Monad m, Traversable t)
+        => (t (Cofree t c) -> m c) -- ^ algebra
+        -> (a -> m (t a))          -- ^ coalgebra
+        -> a -> m c
+dynaM'' phi psi = return . extract <=< hyloM f psi
   where f = liftM2 (:<) <$> phi <*> return
 
--- | dynamorphism on combination variant of ana to histo
-dynaM :: forall m t a c. (Monad m, Traversable (Base t), Recursive t, Corecursive t)
-      => (Base t (Cofree (Base t) c) -> m c) -- ^ algebra
-      -> (a -> m (Base t a))                 -- ^ coalgebra
-      -> a -> m c
-dynaM phi psi = (histoM phi :: t -> m c) <=< (anaM psi :: a -> m t)
+codynaM :: (Monad m, Traversable t)
+        => (t b -> m b)            -- ^ algebra
+        -> (a -> m (t (Free t a))) -- ^ coalgebra
+        -> a -> m b
+codynaM phi psi = chronoM' (phi . fmap extract) psi
 
 -- | codynamorphism on combination variant of histo to ana
-codynaM :: (Monad m, Corecursive c, Traversable (Base c), Traversable (Base t), Recursive t)
-        => (Base t (Cofree (Base t) a) -> m a) -- ^ algebra
-        -> (a -> m (Base c a))                 -- ^ coalgebra
-        -> t -> m c
-codynaM phi psi = anaM psi <=< histoM phi
+codynaM' :: (Monad m, Corecursive c, Traversable (Base c), Traversable (Base t), Recursive t)
+         => (Base t (Cofree (Base t) a) -> m a) -- ^ algebra
+         -> (a -> m (Base c a))                 -- ^ coalgebra
+         -> t -> m c
+codynaM' phi psi = anaM psi <=< histoM phi
+
+codynaM'' :: (Monad m, Traversable t)
+          => (t b -> m b)            -- ^ algebra
+          -> (a -> m (t (Free t a))) -- ^ coalgebra
+          -> a -> m b
+codynaM'' phi psi = hyloM phi g . Pure
+  where g (Pure  a) = psi a
+        g (Free fb) = return fb