We analyze a modified version of the Mini finite element (or the Mini* finite element) for the Stokes problem in R-2 or R-3. The cross-grid element of order one in R-3 is also analyzed. The stability is verified with the aid of the macroelement technique introduced by Stenberg. Each of these methods converges with first order in h as the Mini element does. Numerical tests are given for the Mini* element in comparison with the Mini element when Omega is a unit square on R-2.