Behavioral testing offers a crucial means of diagnosing linguistic errors and assessing capabilities of NLP models. However, applying behavioral testing to machine translation (MT) systems is challenging as it generally requires human efforts to craft references for evaluating the translation quality of such systems on newly generated test cases. Existing works in behavioral testing of MT systems circumvent this by evaluating translation quality without references, but this restricts diagnosis to specific types of errors, such as incorrect translation of single numeric or currency words. In order to diagnose general errors, this paper proposes a new Bilingual Translation Pair Generation based Behavior Testing (BTPGBT) framework for conducting behavioral testing of MT systems. The core idea of BTPGBT is to employ a novel bilingual translation pair generation (BTPG) approach that automates the construction of high-quality test cases and their pseudoreferences. Experimental results on various MT systems demonstrate that BTPGBT could provide comprehensive and accurate behavioral testing results for general error diagnosis, which further leads to several insightful findings. Our code and data are available at https: //github.com/wujunjie1998/BTPGBT.