  The magnetic properties of the two-dimensional $J_{1}-J_{2}$ model with both
exchanges $J_{1}$ and $J_{2}$ being antiferromagnetic and a single-ion
anisotropy at nonzero temperature are investigated. As $J_{2}/J_{1}<1/2$
($>1/2$), only the N\'{e}el (collinear) state exists. When $J_{2}/J_{1}=1/2$,
both the N\'{e}el and collinear states can exist and have the same N\'{e}el
temperature. The calculated free energies show that there can occur a phase
transition between the two states below the N\'{e}el point when the single-ion
anisotropy is strong enough. It is a first-order transition at nonzero
temperature. It is possible that the doping in real materials can modify the
ratio of $J_{2}/J_{1}$ to reach $1/2$ so as to implement the phase transition.
