A two-step renormalization group approach - a decimation followed by a
mean field renormalization group (MFRG) - is applied for calculations
of the critical couplings and critical exponents in two and three dim
ensions in the spin-1/2 anisotropic Heisenberg model. The values of th
e critical parameters are shown to be in good agreement with the serie
s results and are also compared with the results of separate decimatio
n or MFRG calculations.