A regular refraction wave structure may appear when a shock coming from infinity hits an interface between two different media. In such a case, the interface will be deflected, the incident shock will refract, and some reflected wave arises. If the incoming flow and the incident shock are specifically presented, then the refraction shock can be transonic and the reflection wave can be a rarefaction wave. For such a wave pattern, we show that it is conditionally and locally stable provided that a pressure condition, which is determined by the incoming flow, is presented in downstream behind the refraction shock.