This paper presents the constituent-based approach for aligning bilingual multiword expressions, such as noun phrases, by considering the relationship not only between source expressions and their target translation equivalents but also between the expressions and constituents of the target equivalents. We only considered the compositional preferences of multiword expressions and not their idiomatic usages because our multiword identification method focuses on their collocational or compositional preferences. In our experimental results, the constituent-based approach showed much better performances than the general method for extracting bilingual multiword expressions. For our future work, we will examine the scoring method of the constituent-based approach in regards to having the best performance. Moreover, we will extend target entries in the evaluation dictionaries by considering their synonyms.