This　paper　deals　with　the　design　and　analysis　of　adaptive　wavelet　method　for　the　Stokes　problem.　First,　the　limitation　of　Richardson　iteration　is　explained　and　the　multiplied　matrix　M　(0)　in　the　paper　of　Bramble　and　Pasciak　is　proved　to　be　the　simplest　possible　in　an　appropiate　sense.　Similar　to　the　divergence　operator,　an　exact　application　of　its　dual　is　shown;　Second,　based　on　these　above　observations,　an　adaptive　wavelet　algorithm　for　the　Stokes　problem　is　designed.　Error　analysis　and　computational　complexity　are　given;　Finally,　since　our　algorithm　is　mainly　to　deal　with　an　elliptic　and　positive　definite　operator　equation,　the　last　section　is　devoted　to　the　Galerkin　solution　of　an　elliptic　and　positive　definite　equation.　It　turns　out　that　the　upper　bound　for　error　estimation　may　be　improved.