  We construct a cellular basis of the walled Brauer algebra which has similar
properties as the Murphy basis of the group algebra of the symmetric group. In
particular, the restriction of a cell module to a certain subalgebra can be
easily described via this basis. Furthermore, the mixed tensor space possesses
a filtration by cell modules -- although not by cell modules of the walled
Brauer algebra itself, but by cell modules of its image in the algebra of
endomorphisms of mixed tensor space.
