Receiver Autonomous Integrity Monitoring (RAIM) is a method implemented within the receiver to protect users against satellite navigation system failures. For a receiver to execute a RAIM calculation, two conditions must be met: a minimum number of satellites and adequate satellite geometry. The non-existence of the minimum number of satellites (five) is referred to as a RAIM hole. Current regional and global RAIM availability studies use spatial (grid-based) and temporal sampling intervals driven by a trade-off between accuracy and computation workload. The implication of minimising computational load is that accuracy is compromised and potential RAIM holes remain un-sampled, with potential risk to safety. This paper proposes a direct and computationally efficient method (as opposed to the grid-based search approach) to predict RAIM holes. The method is based on the precise computation of satellite coverage (footprint) boundaries, the intersection points and analysis of the topology of the regions of intersection. Test results show that the proposed method is highly accurate and requires minimal computational load compared to the current approach.