FeNi/FeMn bilayers were grown in a magnetic field and subjected to heat treatments at temperatures of 50 to 350 degrees C in vacuum or in a gas mixture containing oxygen. In the as-deposited state, the hysteresis loop of 30 nm FeNi layer was shifted. Low temperature annealing leads to a decrease of the exchange bias field. Heat treatments at higher temperatures in gas mixture result in partial oxidation of 20 nm thick FeMn layer leading to a nonlinear dependence of coercivity and a switching field of FeNi layer on annealing temperature. The maximum of coercivity and switching field were observed after annealing at 300 degrees C.