A fully parallel thinning algorithm may be considered to be constructed in two stages: (i) the definition of edge pixels which can be sequentially removed; and (ii) the definition of protection guards which ensures that the parallel thinning of pixels does not involve destructive interference — for example, the complete removal of a pattern. The goal of this article is to modify the protection conditions of Wu and Tsai's algorithm (1992) and to prove that the resulting method is free from undesirable parallel interactions.