Following the work of \n D. Hilbert\en, the author presents the predicate calculus with the $\varepsilon$-operator, where Ackermann's axiom is taken as one of the axioms. The author interprets the $\varepsilon$-operator as a choice function, and under this semantics he proves that the calculus is strongly complete. In addition the author proves the independence of Ackermann's axiom.