Receiver Autonomous Integrity Monitoring (RAIM) provides an integrity service for Global Navigation Satellite Systems (GNSS). The conventional RAIM algorithm is based on the assumption of a single fault and typically uses the forward-backward method, which is based on thew-test or correlation analysis methods, to exclude the faults. It is suitable for single fault detection and exclusion, while it can lead to inefficiency, can be misleading and can even fail in the exclusion of multiple faults. To solve this problem, an improved method based on consensus voting of thew-test and correlation analysis methods is presented. To verify the performance of the improved method, tests using Global Positioning System (GPS)/BeiDou System (BDS) data have been carried out in comparison with the conventional methods in terms of false and correct faults exclusion rate and computational complexity in the case of a different number of faults. Results show that the improved method has almost the same correct exclusion rate compared to the conventional RAIM in the case of a single fault. It is worth noting that the improved method has a higher correct exclusion probability and computational efficiency as well as a lower possibility of false exclusion in the case of multiple faults.