Let \(A\) be a finite dimensional algebra over a field. The main result of the paper asserts that if \(A\) is representation-finite symmetric then the homotopy category \(K^b(\mathrm{proj\,}A)\) of bounded complexes of projective \(A\)-modules is tilting-connected, that is, the action of iterated irreducible tilting mutation on this category is transitive. In fact, a stronger assertion is proved: the category \(K^b(\mathrm{proj\,}A)\) is silting-discrete, provided \(A\) is a representation-finite symmetric algebra. The theorem is obtained within the frames of the theory of silting mutations for self-injective algebras, introduced by T. Aihara and O. Iyama [“Silting mutation in triangulated categories”, arXiv:1009.3370]. Another important result is a silting version of the classical Bongartz’s Lemma on partial tilting modules.