Unlike wheeled robots, humanoid robots are able to overcome obstacles in the environment by stepping over or upon them. Conventional 2D methods for robot navigation fail to exploit this unique ability of humanoids and thus design trajectories only by circumventing obstacles. Recently, globalized algorithms have been presented that take into account this feature of humanoids. However, due to high computational complexity, most of them are very time consuming. In this paper we present a new approach to footstep planning in obstacle cluttered environments that employs a human-like strategy to terrain traversal. Simulation results of its implementation on a model of Saika-3 humanoid robot are also presented. The algorithm, being one of reactive nature, refutes previous claims that reactive algorithms fail to find successful paths in complex obstacle cluttered environments.