Based on a few historical materials in a book of the Tang dynasty, a calendar, named the Jiayin taiyi li(甲寅太乙曆), is found. It may be the first calendar of taiyi method(太乙術數). Because of its fundamental constants and epoch of month and year are the same with Yin li(殷曆), the arrangement of qi(氣)and the new moon of Jiayin taiyi li must be the same as Yin li. The Jiayin taiyi li was probably compiled around 400 BC, at latest it appeared before 128 BC. The superior epoch of this calendar composed of three big cycles which are 4560 years for the cycle of year and month, 4320 years for the cycle of dayou taiyi(大游太乙) and 225 years for the cycle of wufu taiyi(五福太乙). The last two cycles were never included in the calendar of government. It shows us that the calendar used in the taiyi method is different from the calendar issued by government. Because the selection method of its superior epoch in the taiyi li is the traditional method of ancient Chinese mathematical astronomy, the calendar of taiyi is an important branch of history of Chinese calendrics, which has been neglected by historian for many years.