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This paper proposes a new efficient partial matching algorithm, called Island Driven Partial Matching (IDPM) based on Continuous Dynamic Programming (CDP), to realize flexible retrieval from a speech database by query speech. IDPM enables detecting the sections in the speech database which match partial sections of the query speech efficiently. IDPM applies CDP to short and constant length of unit reference patterns, which are composed of the query speech, and finds the best matching island sections in the speech database. Arbitrary lengths of similar sections are detected by only checking those islands sections. Some experiments were conducted for conversational speech and the results showed IDPM enables the fast matching between arbitrary sections of the reference pattern and the input speech without declining the performance in detecting similar sections compared with our former method.