Abstract: This paper studied the characterization of non-linear isometries between infinite dimensional Banach spaces.Under the assumption that the range space is strictly convex, it was proved that f:X-->Y is an isometry <＝＝> it preserves the distance a,b,ma+nb for a,b∈R⁺, m,n∈N. Thus in some sense the Aleksandrov
problem was solved.

Key words: isometries, strictly convex, distance a preserving map