This paper describes a new O(N 3 2 log(N)) solver for the symmetric positive definite Toeplitz system T N x N = b N . The method is based on the block QR decomposition of T N accompanied with Levinson algorithm and its generalized version for solving Schur complements S m of size m. In our algorithm we use a formula for displacement rank representation of the S m in terms of generating vectors of the matrix T N , and we assume that N = lm with l, m ∈ N. The new algorithm is faster than the classical O(N 2 )-algorithm for N > 2 9 . Numerical experiments confirm the good computational properties of the new method.