We carry out a new study of quark mass matrices M-u (up-type) and M-d (down-type) which are Hermitian and have four zero entries, and find a new part of the parameter space which was missed in the previous works. We identify two more specific four-zero patterns of M-u and M-d with fewer free parameters, and present two toy flavor-symmetry models which can help realize such special and interesting quark flavor structures. We also show that the texture zeros of M-u and M-d are essentially stable against the evolution of energy scales in an analytical way by using the one-loop renormalizaidon-group equations. (C) 2015 The Authors. Published by Elsevier B.V.