Motivated by the recent computations of the quasinormal frequencies of higher dimensional black holes, we exactly calculate the quasinormal frequencies of the Dirac field, propagating in D-dimensional (D ¸ 4) massless topological black hole. From the exact values of the quasinormal frequencies for the fermion and boson fields we discuss whether the recently proposed bound on the relaxation time of a perturbed thermodynamical system is satisfied in the D-dimensional massless topological black hole. Also we study the consequences of these results.MOTIVATED BY THE RECENT COMPUTATIONS OF THE QUASINORMAL FREQUENCIES OF HIGHER DIMENSIONAL BLACK HOLES, WE EXACTLY CALCULATE THE QUASINORMAL FREQUENCIES OF THE DIRAC FIELD, PROPAGATING IN D-DIMENSIONAL (D ¸ 4) MASSLESS TOPOLOGICAL BLACK HOLE. FROM THE EXACT VALUES OF THE QUASINORMAL FREQUENCIES FOR THE FERMION AND BOSON FIELDS WE DISCUSS WHETHER THE RECENTLY PROPOSED BOUND ON THE RELAXATION TIME OF A PERTURBED THERMODYNAMICAL SYSTEM IS SATISFIED IN THE D-DIMENSIONAL MASSLESS TOPOLOGICAL BLACK HOLE. ALSO WE STUDY THE CONSEQUENCES OF THESE RESULTS.