Generalized arc consistency (GAC) plays a central role in solving the constraint satisfaction problem. Table constraints can theoretically represent all kinds of constraint relations, and many algorithms have been proposed to establish GAC on table constraints in the past decade. Among these methods, the simple tabular reduction algorithms (STR) are very efficient. However, the existing STR algorithms are suitable for only positive table constraints. They can not directly work on negative table constraints. In this paper, a STR algorithm, called STR-N, is first proposed to directly work on negative table constraints. Then, two improved versions of STR-N, STR-N2 and STR-NIC are presented. Experimental results show that the STR-N algorithms bring improvements over CPU time while solving the instances with negative table constraints.