Due to the sequential nature of the successive-cancellation (SC) algorithm, the decoding of polar codes suffers from significant decoding latencies. Fast SC decoding is able to speed up the SC decoding process, by implementing parallel decoders at the intermediate levels of the SC decoding tree for some special nodes with specific information and frozen bit patterns. To further improve the parallelism of SC decoding, this paper present a new class of special nodes composed of a sequence of rate one or single-parity-check (SR1/SPC) nodes, which can be easily found especially in high-rate polar code and is able to envelop a wide variety of existing special node types. Then, we analyse the parity constraints caused by the frozen bits in each descendant node, such that the decoding performance of the SR1/SPC node can be preserved once the parity constraints are satisfied. Finally, a generalized fast decoding algorithm is proposed to decode SR1/SPC nodes efficiently, where the corresponding parity constraints are taken into consideration. Simulation results show that the proposed decoding algorithm of the SR1/SPC node can achieve near-ML performance, and the overall decoding latency can be reduced by 43.8% as compared to the state-of-the-art fast SC decoder.