To solve a symmetric positive semi-definite (SPSD) linear system using the FETI method, it is necessary to first compute the null space and then deflate it out. In the FETI (or dual interface domain decomposition) formulation, the null space of a SPSD matrix can be determined from the null space of the reduced coarse grid operator. To accurately solve the original SPSD system, the null space of the reduced coarse grid operator must be computed accurately. In this talk a stable algorithm for computing the null space of the reduced operator using the Lanczos algorithm will be presented. The effectiveness of the new algorithm will be illustrated using several complex structures.