In isothermal models of the expanding solar corona there exists in general an exobase level where the collision mean free path becomes equal to the density scale height. At this level the hydrodynamic approximations of the transport equations fail to be justified and a kinetic approach is more appropriate. This exobase is located below the altitude of the critical point proper to the hydrodynamic solutions. The bulk velocity at the exobase is subsonic and smaller than the expansion velocity at the critical point. Therefore the transition to a supersonic solar wind velocity occurs in the collisionless ion-exosphere.