diff --git a/GPy/kern/_src/rbf.py b/GPy/kern/_src/rbf.py
index f4fb2ad5..d7d1554d 100644
--- a/GPy/kern/_src/rbf.py
+++ b/GPy/kern/_src/rbf.py
@@ -29,7 +29,7 @@ class RBF(Stationary):
         self.use_invLengthscale = inv_l
         if inv_l:
             self.unlink_parameter(self.lengthscale)
-            self.inv_l = Param('inv_lengthscale',1./self.lengthscale**2, Logexp())
+            self.inv_l = Param('inv_lengthscale',1./self.lengthscale, Logexp())
             self.link_parameter(self.inv_l)
 
     def K_of_r(self, r):
@@ -56,7 +56,7 @@ class RBF(Stationary):
         return self.variance*np.sqrt(2*np.pi)*self.lengthscale*np.exp(-self.lengthscale*2*omega**2/2)
     
     def parameters_changed(self):
-        if self.use_invLengthscale: self.lengthscale[:] = 1./np.sqrt(self.inv_l+1e-200)
+        if self.use_invLengthscale: self.lengthscale[:] = 1./(self.inv_l+1e-200)
         super(RBF,self).parameters_changed()
 
     #---------------------------------------#
@@ -80,7 +80,7 @@ class RBF(Stationary):
         self.variance.gradient = dL_dvar
         self.lengthscale.gradient = dL_dlengscale
         if self.use_invLengthscale:
-            self.inv_l.gradient = dL_dlengscale*(self.lengthscale**3/-2.)
+            self.inv_l.gradient = dL_dlengscale*(-self.lengthscale**2)
 
     def gradients_Z_expectations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior):
         return self.psicomp.psiDerivativecomputations(self, dL_dpsi0, dL_dpsi1, dL_dpsi2, Z, variational_posterior)[2]
@@ -90,8 +90,8 @@ class RBF(Stationary):
     
     def update_gradients_diag(self, dL_dKdiag, X):
         super(RBF,self).update_gradients_diag(dL_dKdiag, X)
-        if self.use_invLengthscale: self.inv_l.gradient =self.lengthscale.gradient*(self.lengthscale**3/-2.)
+        if self.use_invLengthscale: self.inv_l.gradient =self.lengthscale.gradient*(-self.lengthscale**2)
 
     def update_gradients_full(self, dL_dK, X, X2=None):
         super(RBF,self).update_gradients_full(dL_dK, X, X2)
-        if self.use_invLengthscale: self.inv_l.gradient =self.lengthscale.gradient*(self.lengthscale**3/-2.)
+        if self.use_invLengthscale: self.inv_l.gradient =self.lengthscale.gradient*(-self.lengthscale**2)