Two components of the spin torque exerted on a free ferromagnetic layer of finite thickness and a half-infinite ferromagnetic electrode in single tunnel junctions have been calculated in the spin-polarized free-electron-like one-band model. It has been found that the torque oscillates with the thickness of ferromagnetic layer and can be enhanced in the junction with the special layer thickness. The bias dependence of torque components also significantly changes with layer thickness. It is non-symmetric for the normal torque, in contrast to the symmetric junctions with two identical half-infinite ferromagnetic electrodes. The asymmetry of the bias dependence of the normal component of the torque can be also observed in the junctions with different spin splitting of the electron bands in the ferromagnetic electrodes.