Although the use of Hamilton's [Hamilton, J.D., 1989. A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica 54, 357–384.] Markov-switching model to date U.S. business cycles has recently gained respect as a reliable tool, the model failed to date the business cycle of Taiwan, a developing country, since model-dated recession indicated a recession for the whole post-1990 period, which clearly is not true. A lot of effort has been devoted to solve this identification problem of Taiwan's business chronology, but, even so, the puzzle remains. This paper uses an extended multivariate Markov-switching factor model to solve this puzzle. We first consider a second-state variable, the variance, in addition to the conventional one-state variable, the mean. We then employ four variables to assist in the identification of the business cycles. It is determined that the new model successfully dates Taiwan's business cycles.