This working paper reformulates the Spiess and Florian frequency-based transit assignment method in matrix algebra revealing a new solution method. It is shown that the number of destination-specific passenger wait times at stops is equal to the number of flow conservation constraints (Proposition 1). The frequency-based transit assignment is found by matrix manipulation and when there are line capacity constraints the equilibrium effective frequencies are obtained iteratively. The existence of equilibrium effective frequencies is proven (Proposition 2). It is shown that a wider range of fare schemes, for example flat fares, can be modeled by the use of legs in the network representation. Numerical examples are presented and solved by R code
