In a previous paper we developed a matrix theory that applies to any cylindrically symmetric fiber surrounded by Bragg cladding. Using this formalism, along with Finite Difference Time Domain (FDTD) simulations, we study the waveguide dispersion for the m = 1 mode in an air-core Bragg fiber and showed it is possible to achieve very large negative dispersion values (~ -20,000 ps/(nm.km)) with significantly reduced absorption loss and non-linear effects.