The aviation community is actively pursuing advanced receiver autonomous integrity monitoring (ARAIM) to enhance the safety of aircraft navigation services. Protection level calculation is a crucial task in the solution separation-based ARAIM as it determines the availability of the ARAIM. Accurately determining the worst-case fault bias (WCFB) is beneficial in improving the bounding tightness of protection level on positioning error. Unfortunately, the WCFB determination is a challenging task that requires a time-consuming searching procedure, especially when dealing with the multi-satellite faults. The traditional ARAIM protection level is achieved by constructing an over-conservative worst-case positioning error bound to avoid the unacceptable time-consumption of the brute-force searching for multi-satellite WCFBs. However, this approach comes at the cost of losing the tightness of the protection level and the availability of the ARAIM. The ARAIM milestone reports have pointed out that the availability of the baseline ARAIM needs to be continuously improved in order to satisfy the worldwide localizer precision vertical 200 (LPV-200) requirements. In response, this paper proposes a novel multi-satellite WCFBs searching method for the ARAIM to improve the tightness of protection level. The method consists of determining the worst-case fault direction and constructing an efficient WCFBs searching procedure. GPS/Galileo dual-constellation simulation result demonstrates that the proposed method not only can improve the availability of the ARAIM up to 9.33% when compared with the traditional method, but also achieves comparable computation efficiency.