We introduce a new stable MINI-element pair for incompressible Stokes equations onquadrilateral meshes, which uses the smallest number of bubbles for the velocity. Thepressure is discretized with the P1-midpoint-edge-continuous elements and each component of the velocity field is done withthe standard Q1-conforming elements enriched byone bubble a quadrilateral. The superconvergence in the pressure of the proposed pair isanalyzed on uniform rectangular meshes, and tested numerically on uniform and non-uniformmeshes.