A method other than the extended-boundary-condition method (EBCM) to compute the T matrix for electromagnetic scattering is presented. The separation-of-variables method (SVM) is used to solve the electromagnetic scattering problem for a spheroidal particle and to derive its T matrix in spheroidal coordinates. A transformation is developed for transforming the T matrix in spheroidal coordinates into the corresponding T matrix in spherical coordinates. The T matrix so obtained can be used for analytical calculation of the optical properties of ensembles of randomly oriented spheroids of arbitrary shape by use of an existing method to average over orientational angles. The optical properties obtained with the SVM and the EBCM are compared for different test cases. For mildly aspherical particles the two methods yield indistinguishable results. Small differences appear for highly aspherical particles. The new approach can be used to compute optical properties for arbitrary values of the aspect ratio. To test the accuracy of the expansion coefficients of the spheroidal functions for arbitrary arguments, a new testing method based on the completeness relation of the spheroidal functions is developed.