Abstract: An orthogonal BSP (binary space partitioning) tree is a commonly used spatial subdivision data structure for ray tracing acceleration. While the construction of a BSP tree takes a relatively short time, the efficiency of a traversal algorithm significantly influences the overall rendering time. We propose a new fast traversal algorithm based on statistical evaluation of all possible cases occurring during traversing a BSP tree. More frequent cases are handled simply, while less frequent ones are more computationally expensive. The proposed traversal algorithm handles all singularities correctly. The algorithm saves from 30% up to 50% of traversal time comparing with the commonly-known Sung and Arvo algorithms.