We show that properly detuning the carrier frequency of each of the criss-cross bichromatic waves from the transition frequency in the atom, it is possible to form a two-dimensional trap for atoms if the intensity of the waves is sufficiently large. For zero and near zero initial phases of waves, and also for π and near π phase shift between criss-cross waves a dynamic spatial structure of square cells with the side λ/ √ 2 is formed. Numerical simulations are carried out for sodium atoms.