Abstract: In this paper, we study a class of factorized indefinite preconditioning techniques for solving linear system Ax=b, where A is sparse and symmetric indefinite. Choosing an appropriate pivoting strategy is the key for the success of factorization for an indefinite matrix. To speed up the process for selecting the pivot, we propose a relaxed bounded Bunch-Kaufman (RBBK) algorithm, analyze its stability, and derive the criteria for parameter selection. Combining RBBK algorithm with the incomplete Cholesky factorization, we obtain a kind of stable preconditioning technique via modified incomplete Cholesky factorization. Preconditioned by this kind of preconditioners, SQMR iteration converges very fast according to the presented numerical examples.