  Let E be a number field and G be a finite group. Let A be any O_E-order of
full rank in the group algebra E[G] and X be a (left) A-lattice. In a previous
article, we gave a necessary and sufficient condition for X to be free of given
rank d over A. In the case that (i) the Wedderburn decomposition of E[G] is
explicitly computable and (ii) each component is in fact a matrix ring over a
field, this led to an algorithm that either gives elements that either gives an
A-basis for X or determines that no such basis exists. In the present article,
we generalise the algorithm by weakening condition (ii) considerably.
