Crossover from classical to quantum regimes of the barrier transition rate in a biaxial ferromagnetic magnet with a magnetic field applied along hard anisotropy axis is investigated. We show that the type of action-temperature diagrams can be determined by counting the number of bifurcation points. The model possesses not only the known type Ⅰ and Ⅱ, but also the interesting type Ⅲ and Ⅳ of transition which do not occur in general.