ABSTRACT: In this paper we develop a new Generalized Quasidiffusion (GQD) method to accelerate the iterative convergence of SN particle transport problems. The standard Quasidiffusion (QD) or Variable Eddington Factor (VEF) method converges rapidly but is inconsistent – its solution differs by truncation errors from the SN solution. The widely-used Coarse Mesh Finite Difference (CMFD) and Diffusion Synthetic Acceleration (DSA) methods are consistent and converge rapidly for optically thin spatial cells, but typically become unstable for optically thicker cells. The new GQD method possesses the positive features of these existing methods, but avoids their shortcomings. Like CMFD and DSA, the GQD method is consistent – it produces the same converged solution as the unaccelerated SN equations. And, like QD, the GQD method is unconditionally stable for problems with spatial cells of any optical thickness. The standard QD method employs Eddington factors that render the QD solution consistent only when the optical thickness of the spatial cells limits to 0. The GQD method employs new “consistent” Eddington factors that make the GQD solution consistent for any spatial grid. The new consistent Eddington factors must be estimated within each iteration. This estimation is inexpensive, but there are issues with it, which we discuss. In this paper, the new GQD method is derived and tested on simple 1-D problems. Our theoretical and experimental results support the assertion that the GQD method is consistent and unconditionally stable.