A fully discrete version of the velocity-correction method, proposed
in \cite{Shen03v} for the time-dependent Navier-Stokes equations, is
introduced and analyzed. It is shown that, when accounting for space
discretization, additional consistency terms, which vanish when space
is not discretized, have to be added to establish stability and
optimal convergence.  Error estimates are derived for both the
standard version and the rotational version of the method.  These error
estimates are consistent with those in \cite{Shen03v}
as far as time discretiztion is concerned
and are optimal in space for finite elements satisfying the
inf-sup condition.