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In this letter, a novel approach to approximate calculation of Karhunen-Loève transform (KLT) is proposed. It is proved that with the practical assumptions the maximization of the sum of fourth-order moments of random variables in the domain of orthonormal transform leads to any permuted KLT. On the basis of theoretical results, we derive and formulate the gradient method of adaptation of orthonormal parametric transforms. The main qualities of the proposed method are: computational efficiency, high repeatability of results, independence of target processing schemes, an unsupervised adaptation of transform parameters in on-line learning mode based on incoming vectors of input samples. Experimental studies confirm practical effectiveness of the method when applied to adaptation of fast parametric orthonormal transforms.