We present here an exact integral representation of solutions of the wave equation with constant coefficients in two spatial dimensions in terms of localized solutions. A solution is given as a superposition of localized solutions each of which lives in the reference system, which moves in the x direction with velocity v. To obtain any solution, we must take into account all |v| ≤ c, where c is the velocity of wave propagation, and use also shifts and scaling. The representation is constructed by means of space-temporal wavelet theory which is applied to the section of a solution in the plane y = 0.