The effect of an applied magnetic field on the temperature at the maximum of the zero-field-cooled (ZFC) magnetization, M_ZFC , is studied using the recently obtained analytic results of Coffey et al (Coffey W T et al 1998 Phys. Rev. Lett. 80 5655) for the prefactor of the Néel relaxation time which allow one to precisely calculate the prefactor in the Néel-Brown model and thus the blocking temperature as a function of the coefficients of the Taylor series expansion of the magnetocrystalline anisotropy. The present calculations indicate that even a precise determination of the prefactor in the Néel-Brown theory, which always predicts a monotonic decrease of the relaxation time with increasing field, is insufficient to explain the effect of an applied magnetic field on the temperature at the maximum of the ZFC magnetization. On the other hand, we find that the non-linear field dependence of the magnetization along with the magnetocrystalline anisotropy appears to be of crucial importance to the existence of this maximum.