A disconnectedness problem which appeared in the 1‐subcycle parallel thinning algorithm [1] is shown and a correct condition is presented to overcome this problem. As a result, to preserve the connectivity of a P8ET‐type thin line, the removal of a (quasi) T‐junction should be guaranteed by its neighbors that do not belong to any one of the commonly used subwindows, mutually opposite subwindows, and T‐junction cases.