As a strategy to further reduce the transmission pressure during the peak traffic times in wireless network, coded caching has been widely studied recently. And several coded caching schemes are constructed focusing on the two core problems in practice, i.e., the rate transmitted during the peak traffic times and the packet number of each file divided during the off peak traffic times. It is well known that there exits a tradeoff between the rate and the packet number. In this paper, a novel recursive construction is proposed. As an application, several new schemes are obtained. Comparing with previously known schemes, new schemes could further reduce packet number by increasing little rate. And for some parameters in coded caching systems, the packet number of our new schemes are smaller than that of schemes generated by memory sharing method which is widely used in the field of caching. By the way our new schemes include all the results constructed by Tang et al., (IEEE ISIT, 2790-2794, 2017) as special cases.