It is proved that the CG coefficient of the permutation group and the outer-product reduction coefficient are just the coupling coefficient which couple the irreduci-ble basis of any SU(m) and SU(n), to those of SU(mn)?SU(m)× SU(n) and SU(m+n)?SU(m)?SU(n) respectively. Several simple methods are given for the calculation of the irreducible bases of SU(mn)?SU(m) × SU(n) and SU(m+n) ?SU(m)?SU(n) when using the Gelfand representation of SU(mn) and SU(m+n). The SU(6)?SU(3) × SU(2) and SU(8)?SU(4) × SU(2) baryon wave functions commonly used in elementary particle models are given in detail.