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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 dimensions in the spin-1 anisotropic Heisenberg model. The values of the critical parameters are shown to be in good agreement with the series results and are also compared with the results of separate decimation or MFRG calculations.