  The generalized Weyl transform of index $\alpha$ is used to implement the
time-slice definition of the phase space path integral yielding the Feynman
kernel in the case of noncommutative quantum mechanics. As expected, this
representation for the Feynman kernel is not unique but labeled by the real
parameter $\alpha$. We succeed in proving that the $\alpha$-dependent
contributions disappear at the limit where the time slice goes to zero. This
proof of consistency turns out to be intricate because the Hamiltonian involves
products of noncommuting operators originating from the non-commutativity. The
antisymmetry of the matrix parameterizing the non-commutativity plays a key
role in the cancelation mechanism of the $\alpha$-dependent terms.
