Self-assembled In0.4Ga0.6As quantum dots (QDs) on GaAs (3 1 1)B surface has been grown by atomic hydrogen-assisted molecular beam epitaxy (H-MBE). The lateral ordering and size homogenization of islands is studied by using atomic force microscopy (AFM), fast Fourier transformation (FFT) and auto correlation (AC) spectra. It is revealed that strikingly well-defined square two-dimensional (2D) lattice of InGaAs dots are formed on the GaAs (3 1 1)B surface. This remarkable self-organization behavior is explained by the special ordering mechanism in our material system, originating from the high elastic anisotropy of the GaAs as well as the chosen (3 1 1)B growth orientation.