Irreversible structural relaxation of bulk amorphous Zr52.5Ti5Cu17.9Ni14.6Al10 was studied by means of logarithmic decrement and shear modulus measurements using an inverse torsion pendulum in the frequency range from 5 Hz to 40 Hz. Irreversible contributions to the decrement and shear modulus and their frequency, temperature, and time dependences were investigated. The activation energy spectrum of irreversible structural relaxation has been reconstructed. It has been shown that irreversible structural relaxation can be regenerated by a special heat treatment. The results obtained are discussed within the framework of a phenomenological model, which implies existence of two-well relaxation centers in the glass structure.