Abstract: We calculated the ground state energies, spin wave spectrum, and investigated the stability of the diagonal double stripe and orthogonal double stripe magnetic orderings of the J1 - J2 - J3 Heisenberg square lattice. We assumed a small J1 and J2 <2J3, and analytically calculated the quantum corrections with a four sublattice model. By investigating the spectrum around the goldstone point (π/2, - π/2), we found that the diagonal double stripe phase is unstable. We also considered how the orthogonal double stripe phase, found to be stable, competes with spiral phase. We compared our results to previous simulations and neutron scattering experiments of FeTe, which is thought to have a double stripe phase.