The magnetization angle and thickness dependence of magnetic anisotropy in the exchange-biased [Pd/Co]${ imes}$5/FeMn multilayers with an out-of-plane anisotropy were investigated to determine the origin of perpendicular exchange biasing. As the Co thickness increased to 1.5 nm in the [Pd(0.8 nm)/Co(t)]${ imes}$5/FeMn(120 nm) films, the hysteresis loops were converted from square loops at a thin Co (<0.4 nm) to complicated round ones at a thick Co. The irregularly asymmetric step (IAS) at the left top of the loop appeared in the loop of the 0.6-nm Co film due to an inhomogeneity in the exchange anisotropy. As the Pd thickness increased to 1.6 nm, the step disappeared, and the perpendicular magnetic anisotropy was maximized in the Co thickness between 0.6 and 0.9 nm. The conversion of the magnetization loop along the magnetization angle coincided with the equation $H_{(eff)}=H_o;cos{ heta}$. The IAS of the 0.8-nm Pd film disappeared after thermal annealing up to $200^{circ}C$ under an external magnetic field.