Summary. In this study, an new vector test function is proposed for two-dimenional control volume mixed nite-element methods where discretization of the computational domain is based in triangular elements. The proposed test function has the advantage of allowing for a pressure-eld approximation that is piecewise smooth rather than piece- wise constant. Implementation of the test function, in association with the usual vector shape functions for triangular elements, is described. In the control-volume approach, the product of the test function and the ux approximation (obtained using associate shape functions) are integrated over a lesser volume than the full triangular element. With the proposed test function, a question arises as [...]