  The low-energy properties of the two-dimensional Heisenberg model with
spin-$\frac{1}{2}$ on a square lattice are investigated on the basis of the
local dimer order. The lattice is divided into square blocks consisting of the
quartet of spins. The spin variables and the Heisenberg Hamiltonian are
expressed in terms of the low-energy quartet variables. On the basis of the
Dyson-Maleev representation the spin-wave theory of the quartet state is
developed. The spectrum of the lower magnon excitations consists of three
degenerate modes with the energy gap $\Delta =0.17J$. The ground state energy
per spin $E/N =-0.6J$. This preprint repeats in the main the previous one but
it contains calculations of the basic corrections and therefore has complete
character.
