One of the most challenging tasks for autonomous robots is avoiding unexpected obstacles during their path following operation. Follow the gap method (FGM) is one of the most popular obstacle avoidance algorithms that recursively guides the robot to the goal state by considering the angle to the goal point and the distance to the closest obstacles. It selects the largest gap around the robot, where the gap angle is calculated by the vector to the midpoint of the largest gap. In this paper, a novel obstacle avoidance procedure is developed and applied to a real fully autonomous wheelchair. This proposed algorithm improves the FGM’s travel safety and brings a new solution to the obstacle avoidance task. In the proposed algorithm, the largest gap is selected based on gap width. Moreover, the avoidance angle (similar to the gap center angle of FGM) is calculated considering the locus of the equidistant points from obstacles that create obstacle circles. Monte Carlo simulations are used to test the proposed algorithm, and according to the results, the new procedure guides the robot to safer trajectories compared with classical FGM. The real experimental test results are in parallel to the simulations and show the real-time performance of the proposed approach.