Streaming graphs are drawing increasing attention in both academic and industrial communities as many graphs in real applications evolve over time. Continuous subgraph matching (shorted as CSM) aims to report the incremental matches of a query graph in such streaming graphs. It involves two major steps, i.e., candidate maintenance and incremental match generation, to answer CSM. Throughout the course of continuous subgraph matching, incremental match generation backtracking over the search space dominates the total cost. However, most previous approaches focus on developing techniques for efficient candidate maintenance, while incremental match generation receives less attention despite its importance in CSM. Aiming to minimize the overall cost, we propose two techniques to reduce backtrackings in this paper. We present a cost-effective index CaLiG that yields tighter candidate maintenance, shrinking the search space of backtracking. In addition, we develop a novel incremental matching paradigm KSS that decomposes the query vertices into conditional kernel vertices and shell vertices. With the matches of kernel vertices, the incremental matches can be produced immediately by joining the candidates of shell vertices without any backtrackings. Benefiting from reduced backtrackings, the elapsed time of CSM decreases significantly. Extensive experiments over real graphs show that our method runs faster than the state-of-the-art algorithm orders of magnitude.