A new signature file method, Multi-Frame Signature File (MFSF), is introduced by extending the bit-sliced signature file method. In MFSF, a signature file is divided into variable sized vertical frames with different on-bit densities to optimize the response time using a partial query evaluation methodology. In query evaluation the on-bits of the lower on-bit density frames are used first. As the number of query terms increases, the number of query signature on-bits in the lower on-bit density frames increases and the query stopping condition is reached in fewer evaluation steps. Therefore, in MFSF, the query evaluation time decreases for increasing numbers of query terms. Under the sequentiality assumption of disk blocks, in a PC environment with 30 ms average disk seek time, MFSF provides a projected worst-case response time of 3.54 seconds for a database size of one million records in a uniform distribution multi-term query environment with 1–5 terms per query. Due to partial evaluation, this desired response time is guaranteed for queries with several terms. The comparison of MFSF with the inverted file approach shows that MFSF provides promising research opportunities.