The total spin_states of a N_body system with spin_one bosons have been investigated. The fractional parentage coefficients for the total spin_states with {N} and {N-1,1} symmetries have been derived. These coefficients facilitate greatly the calculation of related matrix elements,they appear as a powerful tool for the establishment of an improved theory for the spinor Bose_Einstein condensation, where the total spin Sand its Z_component S_Zare both conserved.