A modification of the Loitsyanskii integral is proposed as an invariant of three-dimensional decaying homogeneous and isotropic turbulence. As a result, the kinetic energy of a flow, generated in an infinitely large volume by the initial energy spectrum E(k, t = 0), which peaks in the vicinity of the wavenumber k(0) = 1/L(0) = O(1), L being an integral scale, decays with time in accordance with Kolmogorov's (1941) prediction: K = 1/2u(2) proportional to t(-gamma) with gamma = 10/7.