  We obtain error bounds for a modified Chorin-Teman (Euler non-incremental)
method for non inf-sup stable mixed finite elements applied to the evolutionary
Navier-Stokes equations. The analysis of the classical Euler non-incremental
method is obtained as a particular case. We prove that the modified Euler
non-incremental scheme has an inherent stabilization that allows the use of non
inf-sup stable mixed finite elements without any kind of extra added
stabilization. We show that it is also true in the case of the classical
Chorin-Temam method. The relation of the methods with the so called pressure
stabilized Petrov Galerkin method (PSPG) is established. We do not assume
non-local compatibility conditions for the solution.
