We report a combined pyroelectric, dielectic and structural characterization of PZN single crystals in field cooling (FC) run along [001]. The pyroelectric current and the dielectric permittivity show a new characteristic temperature, at T approximate to 370 K, related to a macroscopic competition between two induced ferroelectric tetragonal (T) and monoclinic (M) phases. The phase transition, which starts around TC-R = 385 K, spreads over a large temperature range and some amount of T-phase is still observed at room temperature (RT). The M-T phase mixture, induced below TC-R, is stable after field removal. According to a previous Raman scattering work, a fourfold symmetry of M-domains is proposed; the residual T-phase is stabilized by the coexistence of four symmetry-allowed M-domains arranged around[001]. Our results confirm that in a restricted temperature range (TC-R - 20 K, TC-R + 20 K) the free energy of the relaxor-ferroelectric PZN is almost independent of the direction of polarization and accordingly the material can switch from one polar order to the other.