This paper proposes the groupwise serial cross interference cancellation(GSCIC) algorithm for coherent detection and analyzes the groupwise serial block interference cancellation(GSBIC) and GSCIC algorithm for an asynchronous wideband DS-CDMA system in a single cell over multipath fading channels. In general, the GSIC algorithm can be grouped into two classes: i.e., GSBIC and GSCIC algorithm. In this paper, the proposed GSCIC algorithm is to improve the performance of the GSBIC algorithm. We compare the performance of the GSCIC and existing GSBIC algorithm in a multipath fading channel to that of the existing SIC algorithm. As a result, the performance of GSCIC algorithm is somewhat better compared with the GSBIC algorithm according to reduction factor $R_{f}$ and is similar to that of the SIC algorithm. And also, the GSBIC and GSCIC algorithms have the advantage that it can be analyzed system performance easily, changing the number of users within a user group according to system capacity.