Underdetermined Blind Source Separation(UBSS) is an important issue, for sparse signals, a novel two-step approach for UBSS based on the law of large numbers and minimum intersection angle rule (LM method) is presented. In the first step, the estimation of the mixed matrix is obtained by using the law of large numbers, and the number of source signals is displayed graphically. In the second step, the method of estimating the source signal with the minimum intersection angle rule is proposed. Finally, two simulation results that illustrate the effectiveness of the theoretical results are presented. It has simple principle and good transplantation capability and can be widely applied in various fields of digital signal processing.