We test infinite-dimensional extension of algebra su(k, k) proposed by Fradkin and Linetsky as the candidate for conformal higher spin algebra. Adjoint and twisted-adjoint representations of su(k, k) on the space of this algebra are carefully explored. For k = 2 corresponding unfolded system is analyzed and it is shown to encode Fradkin-Tseytlin equations for the set of all integer spins 1, 2, . . . with infinite multiplicity.