The signature file method is a popular indexing technique used in information retrieval and databases. It excels in efficient index maintenance and lower space overhead. Different approaches for organizing signature files have been proposed, such as sequential signature files, bit-slice files, S-trees, and its different variants, as well as signature trees. In this paper, we extends the structure of signature trees by introducing multiple-bit checkings. That is, during the searching of a signature tree against a query signature sq, more than one bit in sq will be checked each time when a node is encountered. This does not only reduce significantly the size of a signature tree, but also increases the filtering ability of the signature tree. We call such a structure a general signature tree. Experiments have been made, showing that the general signature tree uniformly outperforms the signature tree approach.