We propose a new analysis for the PSPG method applied to the transient Stokes' problem. Stability and convergence are obtained under different conditions on the discretization parameters depending on the approximation used in space. For the pressure we prove optimal stability and convergence only in the case of piecewise affine approximation under the standard condition on the time-step. Finally, we show that the stability problems of the PSPG method can be circumvented using an appropriate discrete reconstruction of the Laplacian operator.