diff --git a/nifty5/operators/mask_operator.py b/nifty5/operators/mask_operator.py
index 189c87cbbd0d262e1a7ada1414501d5920679293..0ff519fbc6aed7b5d99b1830b874277bab683891 100644
--- a/nifty5/operators/mask_operator.py
+++ b/nifty5/operators/mask_operator.py
@@ -16,33 +16,35 @@
 # NIFTy is being developed at the Max-Planck-Institut fuer Astrophysik
 # and financially supported by the Studienstiftung des deutschen Volkes.
 
+import numpy as np
+
 from ..domain_tuple import DomainTuple
 from ..domains.unstructured_domain import UnstructuredDomain
 from ..field import Field
-from ..sugar import full
 from .linear_operator import LinearOperator
 
 
 class MaskOperator(LinearOperator):
-    def __init__(self, domain, target, xy):
-        self._domain = DomainTuple.make(domain)
-        # TODO Takes a field (boolean or 0/1)
-        # TODO Add MultiFields (output MultiField of unstructured domains)
+    def __init__(self, mask):
+        if not isinstance(mask, Field):
+            raise TypeError
 
-        assert len(xy.shape) == 2
-        assert xy.shape[1] == 2
-        self._target = UnstructuredDomain(xy.shape[0])
+        self._domain = DomainTuple.make(mask.domain)
+        self._mask = np.logical_not(mask.to_global_data())
+        self._target = DomainTuple.make(UnstructuredDomain(self._mask.sum()))
 
-        self._xs = xy.T[0]
-        self._ys = xy.T[1]
+    def data_indices(self):
+        return np.indices(self.domain.shape).transpose((1, 2, 0))[self._mask]
 
     def apply(self, x, mode):
         self._check_input(x, mode)
         if mode == self.TIMES:
-            res = x.val[self._xs, self._ys]
+            res = x.to_global_data()[self._mask]
             return Field(self.target, res)
-        res = full(self.domain, 0.)
-        res[self._xs, self._ys] = x.val
+        x = x.to_global_data()
+        res = np.empty(self.domain.shape, x.dtype)
+        res[self._mask] = x
+        res[~self._mask] = 0
         return Field(self.domain, res)
 
     @property
diff --git a/test/test_operators/test_adjoint.py b/test/test_operators/test_adjoint.py
index 116cb3419f33bc6711456f703f0bf73c047e4eee..13fd6650473665a2efe76c75adc52098f9073799 100644
--- a/test/test_operators/test_adjoint.py
+++ b/test/test_operators/test_adjoint.py
@@ -61,6 +61,17 @@ class Consistency_Tests(unittest.TestCase):
         op = ift.HarmonicTransformOperator(sp)
         ift.extra.consistency_check(op, dtype, dtype)
 
+    @expand(product(_p_spaces, [np.float64, np.complex128]))
+    def testMask(self, sp, dtype):
+        # Create mask
+        f = ift.from_random('normal', sp).val
+        mask = np.zeros_like(f)
+        mask[f > 0] = 1
+        mask = ift.Field(sp, mask)
+        # Test MaskOperator
+        op = ift.MaskOperator(mask)
+        ift.extra.consistency_check(op, dtype, dtype)
+
     @expand(product(_h_spaces+_p_spaces, [np.float64, np.complex128]))
     def testDiagonal(self, sp, dtype):
         op = ift.DiagonalOperator(ift.Field.from_random("normal", sp,