Bloom filters have been employed in various fields because of its simple and effective structure in identifying the membership of an input. Since a Bloom filter can produce false positives, the positive results of a Bloom filter should be identified whether the positives are true or not by accessing the original database. A complement Bloom filter (C-BF) was introduced to identify the true positiveness of a given Bloom filter without accessing the original database. A critical problem of the C-BF is that every element included in the complement set of the given set should be programmed into the C-BF. Since the number of elements included in the complement set can be considerably large, the C-BF would require the significant amount of memory. In this paper, we claim that the elements that produce negative results from the given Bloom filter are not necessarily programmed into the C-BF, since Bloom filters never produce false negatives. In other words, we propose the Petit-BF (P-BF) which programs only the elements that cause false positives from the given Bloom filter. Simulation results and theoretical analysis show that the proposed method can achieve the same performance using a considerably smaller amount of memory.