  The quantum-classical transition of the escape rate of the spin model \cal H=
-DS_z^2 - H_zS_z + B S_x^2 is investigated by a perturbative approach with
respect to B [D. A. Garanin, J. Phys A {\bf 24}, L61 (1991)]. The transition is
first order for B<B_c(H_z), the boundary line going to zero as B_c/D ~ 1 -
H_z/(2SD) in the strongly biased limit. The range of the first-order transition
is thus larger than for the model \cal H = -DS_z^2 - H_zS_z - H_x S_x studied
earlier, where in the strongly biased case H_{xc}/(2SD) ~ [1-H_z/(2SD)]^{3/2}.
The temperature of the quantum-classical transition, T_0, behaves linearly in
the strongly biased case for both models: T_0 ~ 2SD - H_z.
