Terrain aided navigation (TAN) is the concept of using terrain height variations below the aircraft to obtain an estimation of the position that is used to limit the error in the INS. A new TAN approach using fading memory is proposed. The basic idea of this approach is using a new type correlation functional value to estimate the navigation position. The correlation function is defined by all the historical measurements with fading memory weight. A set of simulations shows that the method improve the precision and speed of TAN compared with TERCOM.