In this work, a lossless and closed rectangular waveguide partially filled with a slab of transversely magnetized ferrite, without assuming vanishing of the derivative in the direction of the dc biasing field, has been analyzed using Method of Moment (MoM). Generally, there are basically three types of modes in the waveguide: propagating, evanescent and complex modes. To support evanescent mode, the waveguide must be bidirectional. But a rectangular waveguide filled with a slab of ferrite transversely magnetized is not bidirectional, if there exists no sym- metry with respect to the rotation by π about an axis perpendicular to propagation direction. So such a waveguide does not support the evanescent waves. Propagation constant is complex or pure imaginary. Our waveguide is filled with a transversely magnetized gyrotropic medium and does not satisfy the condition of symmetry with respect to the rotation by π about an axis perpendicular to propagation direction. So it is not bidirectional and hence does not support evanescent modes. Results of the MoM are consistent with this situation. In a lossless and closed rectangular waveguide partially filled with a slab of transversely magnetized ferrite, Maxwell’s equations, consisting of partial differential equations, are transformed into an infinite linear alge- braic equation system by application of the Galerkin version of Moment method. As the result of algebraic operations, from the transmission line equations a quadratic eigenvalue problem is obtained whose eigenvalue corresponds to the propagation constant. The determinant of the coefficient matrix of the quadratic eigenvalue problem is a monic polynomial of the propagation constant whose coefficients are rational functions of the complex frequency. If the polynomial is set equal to zero and is multiplied by the common denominator of the coefficients, an algebraic equation is obtained. The roots of this equation are the propagation constants. In this work as the contribution, using algebraic function theory, the solution of the algebraic equation (propaga- tion constant) for the waveguide filled with transversely magnetized ferrite medium, is expressed by means of a Puiseux series in the neighborhood of the algebraic branch point. Puiseux series coefficients are solved using transmission line equations and the propagation constant is com- puted from this series expansion. Puiseux series results are compared and found to conform with MoM results and the exact solution.