Abstract: Stable homotopy regular morphism is defined in this paper by using suspension functor. Its existenceand properties are also presented. The main conclusion is as follows. Letf: X→Y be a map of stable standard decomposition (g,Z,h). Supposing that there exist A,B and i: A→X, p: Y→B such that gi and phare all stable homotopy equivalences, then fis a stable homotopy regular morphism, and f is uniquenessin the sence of kstable homotopy.

Key words: suspension functor, homotopy regular morphism, stable homotopy regular morphism