Motivated by synthesis of new antiferromagnetic compounds with weak exchange coupling, a study of high magnetic field properties of the Heisenberg model on a square-lattice is undertaken here. Ordered spins at zero temperature cant toward the field direction inducing coupling of transverse and longitudinal magnon modes. Resulting interactions renormalize the ground-state energy and the dispersion relation below a threshold field H∗ = 0.76Hsat, where one-magnon excitations starts to become unstable and acquire finite lifetimes. Such decays originates from Van-Hove singularities in the two-magnons density of states lying below the one-particle energy. Decay rates are computed using a Self-Consistent Born Approximation, revealing strong magnon damping in the middle of the Brillouin’s zone quarters whereas sound and precession modes remain well defined. Far from these modes, transverse part of the dynamical structure factor display important broadening of the excitations peaks that might be accesible to neutron scattering experiments.