To address the shortcomings of the existing trend and cycle decomposition methods, we propose a new method based on the MS-FCVAR model. This new method considers the possible long-term memory of economic variables, the fractional cointegrated relationships among variables and their structural changes. Based on the principle of "letting the data speak for themselves", the new method obtains the following findings in the system of real GDP, fixed asset investment, consumption and export, which are consistent with the development history of China's economy. With the fourth quarter of 2010 as the cut-off point, not only has China's economic growth decelerated and shifted gears, but also the growth momentum has shifted. Since the economy entered ‘a new normal’, especially the supply-side reform, the slowdown of China's economic growth is mainly caused by the trend rather than the cycle of GDP. More importantly, compared with the existing decomposition methods, the prediction deviation and mean square error of the new method are the least when making out-of-sample predictions. Overall, the new method has both good robustness and can be widely applied to research on many economic and management problems, such as long-term trend judgment and short-term fluctuation analysis.