The ordering process from short range order to long range order in a Cu-25.7 at%Pt alloy was studied by electron diffraction and dark field microscopy. The alloy as quenched from 923 K was found to give typical diffuse scatterings in the diffraction pattern, indicating that the alloy is short range ordered. When the as-quenched alloy is annealed at 693 K, 793 K or 823 K, the short range order develops at the early stage to a microdomain structure where numerous ordered particles about a few nanometers in diameter are embedded in a disordered matrix. The ordered particles have a long range correlation of antiphase with one another. By further annealing at 693 K or 793 K, the particles grow up to large domains of Ll2 or Ll2-s, respectively, while at 823 K the alloy has an equilibrium state of a mixture of (Al+Ll2-s). The ordering processes observed can be described in general in terms of "evolution of ordering wave". When the ordering wave increases both of its amplitude and wavelength with annealing, Ll2 develops. If the wave increases its amplitude, but maintains its wavelength, Ll2-s, is formed.