A new algorithm for blind source separation is proposed, which only extracts the single independent component at each stage. The single independent component is acquired by an iterative algorithm for searching for the optimal solution of the defined cost function. Moreover, all the independent components are obtained by systematic multistage decomposition and multistage reconstruction. When there is spatially colored noise, the performance of this algorithm is advantageous over jointly approximated diagonalization of eigen-matrices (JADE). Simulated results show that if the number of source signals is more than 25, its computational complexity is lower than that of JADE.