A prescription for the third basis function relevant to an approximate model of neutral particle transport in ducts is given. When a third basis function is included in the model, the full five-variable differential equation that describes time-independent particle transport in a duct is reduced to a three-group-like transport equation in two variables (one spatial, one angular). Numerical results based on the discrete ordinates method for a series of test cases are compared with results from a suitably modified version of the MCNP code to assess the gain in precision of the model with three basis functions relative to previous versions of the model that make use of only one or two basis functions.