The effect of softening of the exchange in a magnetic overlayer (surface) on the temperature dependence of the surface magnetization Ms(T ) in the spin-wave regime is investigated. A recursion method for calculating the surface density of spin-wave states (DOS) is developed. It is applied to a magnetic overlayer of n atomic layers with softened exchange between the layers. The principal result obtained for an overlayer of any thickness between n = 1 and n = 20 is that the surface DOS and, therefore, the temperature dependence of the surface magnetization Ms(T ) are determined by the exchange interactions in the overlayer (surface). The classical result of surface magnetism that M~(T) follows the Bloch T 3/z law but decreases twice as fast as in the bulk breaks down at temperatures as low as 1% of the Curie temperature T c. Above this temperature, there is a rapid crossover to a second extended region of an effective T 3/2 law with a prefactor determined by the surface exchange. This second region of the T 3/2 law which extends up to temperatures T~ 0.4 T c provides a perfect explanation for the observed Ms(T ) which was determined recently by SPLEED for Nia0Fea0B20 surface and by Mrssbauer spectroscopy for Fe(fl0) surface.