In this paper, we study the problem of feedback complete linearization for a given single-input-single-output stochastic nonlinear system. Using the invariance under transformation rule (Pan, Proceedings of the 36th IEEE Conference on decision and control, San Diego, CA, 1997, pp. 24-29), the coordinate-free necessary and sufficient conditions for the solvability of the problem is derived, which is exactly the same as the necessary and sufficient conditions for solvability of the feedback complete linearization problem for an associated deterministic uncertain nonlinear system.