The magnetic excitation spectrum of a YBa2Cu3O7 crystal containing 0.5% of nonmagnetic (Zn) impurities has been determined by inelastic neutron scattering. Whereas in the pure system a sharp resonance peak at E similar or equal to 40 meV is observed exclusively below the superconducting transition temperature T-c, the magnetic response in the Zn-substituted system is broadened significantly and vanishes at a temperature much higher than T-c. The energy-integrated spectral weight observed near q = (pi, pi) increases with Zn substitution, and only about half of the spectral weight is removed at T-c.