Negative sequential patterns (NSP) become increasingly important and most of the existing methods introduce so strict constraints that many meaningful patterns would be lost. In this paper, we loosen these constraints and solve a series of consequent problems. Firstly, negative containment is defined to determine whether a data sequence contains a negative sequence. Secondly, an efficient method to fast calculate the supports of negative sequences is proposed. Finally, a novel and efficient algorithm, NegI-NSP, is proposed to efficiently identify meaningful NSP. Experiments show that NegI-NSP can efficiently obtain more meaningful patterns by directly using existing PSP mining algorithms.