diff --git a/GPy/core/parameterised.py b/GPy/core/parameterised.py
index 81b6aa8a..6e5493ad 100644
--- a/GPy/core/parameterised.py
+++ b/GPy/core/parameterised.py
@@ -94,7 +94,7 @@ class parameterised(object):
         Other objects are passed through - i.e. integers which were'nt meant for grepping
         """
 
-        if type(expr) is str:
+        if type(expr) in [str, np.string_, np.str]:
             expr = re.compile(expr)
             return np.nonzero([expr.search(name) for name in self._get_param_names()])[0]
         elif type(expr) is re._pattern_type:
diff --git a/GPy/kern/Matern52.py b/GPy/kern/Matern52.py
index 84c71089..b3365ec9 100644
--- a/GPy/kern/Matern52.py
+++ b/GPy/kern/Matern52.py
@@ -31,14 +31,14 @@ class Matern52(kernpart):
         self.ARD = ARD
         if ARD == False:
             self.Nparam = 2
-            self.name = 'Mat32'
+            self.name = 'Mat52'
             if lengthscale is not None:
                 assert lengthscale.shape == (1,)
             else:
                 lengthscale = np.ones(1)
         else:
             self.Nparam = self.D + 1
-            self.name = 'Mat32_ARD'
+            self.name = 'Mat52_ARD'
             if lengthscale is not None:
                 assert lengthscale.shape == (self.D,)
             else:
diff --git a/GPy/kern/__init__.py b/GPy/kern/__init__.py
index 20d84949..17bc607e 100644
--- a/GPy/kern/__init__.py
+++ b/GPy/kern/__init__.py
@@ -2,5 +2,5 @@
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
 
-from constructors import rbf, Matern32, Matern52, exponential, linear, white, bias, finite_dimensional, spline, Brownian, rbf_sympy, sympykern, periodic_exponential, periodic_Matern32, periodic_Matern52
+from constructors import rbf, Matern32, Matern52, exponential, linear, white, bias, finite_dimensional, spline, Brownian, rbf_sympy, sympykern, periodic_exponential, periodic_Matern32, periodic_Matern52, product_orthogonal
 from kern import kern
diff --git a/GPy/kern/constructors.py b/GPy/kern/constructors.py
index b483c823..1e76f559 100644
--- a/GPy/kern/constructors.py
+++ b/GPy/kern/constructors.py
@@ -18,7 +18,7 @@ from Brownian import Brownian as Brownianpart
 from periodic_exponential import periodic_exponential as periodic_exponentialpart
 from periodic_Matern32 import periodic_Matern32 as periodic_Matern32part
 from periodic_Matern52 import periodic_Matern52 as periodic_Matern52part
-
+from product_orthogonal import product_orthogonal as product_orthogonalpart
 #TODO these s=constructors are not as clean as we'd like. Tidy the code up
 #using meta-classes to make the objects construct properly wthout them.
 
@@ -241,3 +241,14 @@ def periodic_Matern52(D,variance=1., lengthscale=None, period=2*np.pi,n_freq=10,
     """
     part = periodic_Matern52part(D,variance, lengthscale, period, n_freq, lower, upper)
     return kern(D, [part])
+
+def product_orthogonal(k1,k2):
+    """
+     Construct a product kernel
+     
+    :param k1, k2: the kernels to multiply
+    :type k1, k2: kernpart
+    :rtype: kernel object
+    """
+    part = product_orthogonalpart(k1,k2)
+    return kern(k1.D+k2.D, [part])
diff --git a/GPy/kern/kern.py b/GPy/kern/kern.py
index 5f259f55..692c3874 100644
--- a/GPy/kern/kern.py
+++ b/GPy/kern/kern.py
@@ -6,7 +6,8 @@ import numpy as np
 from ..core.parameterised import parameterised
 from functools import partial
 from kernpart import kernpart
-
+import itertools
+import GPy
 
 class kern(parameterised):
     def __init__(self,D,parts=[], input_slices=None):
@@ -45,7 +46,6 @@ class kern(parameterised):
         for p in self.parts:
             assert isinstance(p,kernpart), "bad kernel part"
 
-
         self.compute_param_slices()
 
         parameterised.__init__(self)
@@ -133,6 +133,67 @@ class kern(parameterised):
         newkern.tied_indices = self.tied_indices + [self.Nparam + x for x in other.tied_indices]
         return newkern
 
+    def __mul__(self,other):
+        """
+        Shortcut for `prod_orthogonal`. Note that `+` assumes that we sum 2 kernels defines on the same space whereas `*` assumes that the kernels are defined on different subspaces.
+        """
+        return self.prod_orthogonal(other)
+
+    def prod_orthogonal(self,other):
+        """
+        multiply two kernels. Both kernels are defined on separate spaces. Note that the constrains on the parameters of the kernels to multiply will be lost.
+        :param other: the other kernel to be added
+        :type other: GPy.kern
+        """
+        K1 = self.copy()
+        K2 = other.copy()
+        K1.unconstrain('')
+        K2.unconstrain('')
+
+        prev_ties = K1.tied_indices + [arr + K1.Nparam for arr in K2.tied_indices]
+        K1.untie_everything()
+        K2.untie_everything()
+
+        D = K1.D + K2.D
+
+        newkernparts = [GPy.kern.product_orthogonal(k1,k2).parts[0] for k1, k2 in itertools.product(K1.parts,K2.parts)]
+
+        slices = []
+        for sl1, sl2 in itertools.product(K1.input_slices,K2.input_slices):
+            s1, s2 = [False]*K1.D, [False]*K2.D
+            s1[sl1], s2[sl2] = [True], [True]
+            slices += [s1+s2]
+
+        newkern = kern(D, newkernparts, slices)
+
+        # create the ties
+        K1_param = []
+        n = 0
+        for k1 in K1.parts:
+            K1_param += [range(n,n+k1.Nparam)]
+            n += k1.Nparam
+        n = 0
+        K2_param = []
+        for k2 in K2.parts:
+            K2_param += [range(K1.Nparam+n,K1.Nparam+n+k2.Nparam)]
+            n += k2.Nparam
+        index_param = []
+        for p1 in K1_param:
+            for p2 in K2_param:
+                index_param += [0] + p1[1:] + p2[1:]
+        index_param = np.array(index_param)
+
+        # follow the previous ties
+        for arr in prev_ties:
+            for j in arr:
+                index_param[np.where(index_param==j)[0]] = arr[0]
+
+        # tie
+        for i in np.unique(index_param)[1:]:
+            newkern.tie_param(np.where(index_param==i)[0])
+
+        return newkern
+
     def _get_params(self):
         return np.hstack([p._get_params() for p in self.parts])