A new method for the first-principles calculation of the transfer matrix is presented. The method is based on a Green-function formulation and allows to relate the wavefunctions and their derivatives on boundaries at opposite sides of a film or junction of finite thickness. Both the underlying theory and an actual implementation in the full-potential linearized augmented planewave (FLAPW) method are described. Applications of the transfer-matrix method include the calculations of the complex bandstructure and the calculation of ballistic electron transport relevant in realistic magnetic multilayers and magnetic tunne1junctions used in spin- and magnetoelectronics.