An absolutely stabilized finite element formulation for the Stokes problem is presented in this paper. This new formulation, which is nonsymmetric but stable without employing of any stability constant, can be regarded as a modification of the formulation porposed recently by

*Th. J. R. Hughes* and

*L. P. Franca* [Comput. Methods Appl. Mech. Eng. 65, 85-96 (1987;

Zbl 0635.76067)]. Optimal error estimates in

${L}^{2}$-norm for the new stabilized finite element approximation of both the velocity and the pressure fields are established, as well as one in

${H}^{1}$-norm for the velocity field.