We show that a one-dimensional photonic crystal containing two kinds of single-negative materials can possess an omnidirectional gap whose edges are insensitive to incident angle and polarization, owing to the unusual field configuration in the structure.In contrast to an omnidirectional gap based on a photonic gap that corresponds to zero averaged refractive index, it can be made very wide by varying the ratio of the thicknesses of two media.Moreover, it is independent of polarization under special parameters.These properties may provide a mechanism to design a broadband omnidirectional reflector with fixed bandwidth.