Abstract: In this paper, by using spherical characteristic function T(r, w), the authors define and establish the existence of a new singular direction for the algebroidal function w, namely a T direction, for which the characteristic function T(r, w) is used as a comparison function. Moreover, the authors prove that the number of exceptional values is at most 2+[δ_x] ≤ 2 ν.

Key words: T direction, Algebroidal function, Characteristic function