In the case of nonzero fermion mass, within a range of Ansatze for the full fermion-boson vertex, we show that Dyson-Schwinger equation for the fermion propagator in QED₃ has two qualitatively distinct dynamical chiral symmetry breaking solutions. As the fermion mass increases and reaches to a critical value m_c, one solution disappears, and the dependence of m_c on the number of fermion flavors is also given.