A theory is described for solving the integral neutron transport equation by the transmission probability method. Detailed attention is given to the problem in rectangular x-y geometry. Within a mesh the neutron flux is assumed to be linearly dependent on the x and y coordinates. The angular dependence is given by a double P1 approximation. At the mesh surfaces a term is considered that allows for an asymmetric flux distribution relative to the surface normal. The inner source is obtained from the equilibrium equation. Based on this method, the code COXY has been developed and applied to one- and two-dimensional rectangular cell calculations. The calculated results show good agreement with those of SN and collision probability codes.