A new method for synthesis of isolated frequencies of composite vibrating systems is presented. First, from an analogy with single-degree-of-freedom systems composed of springs and masses, the essential patterns of synthesis are clearly recognized in regard to the composite, continuous systems to which the well-known Southwell-Dunkerley methods are applicable. Then, in a converse manner, another fundamental pattern of synthesis is formulated for a single-degree-of-freedom model with springs in series, and this leads to a general formulation of the new synthetic method for continuous systems. It can predict a lower limit of the true frequency for such vibrating systems having a series-type coupling of restoring elements. Like the Southwell-Dunkerley methods, it is based on Rayleigh's principle, but in order to obtain an approximate value very close to the correct frequency one further needs another condition, which can be provided on the basis of a perturbation technique, at least in the most general cases. When applied to an ideal composite system whose restoring elements are coupled exactly in series, the present method proves to be essentially equivalent to the previous Southwell-Dunkerley methods in the sense that the additional approximate error, characteristic of the present method, is stationary with respect to slight differences of deflection curves among all isolated systems, as well as the error associated with the Rayleigh approximation. Upon adding the present method to a class of the previous synthetic methods, it becomes possible to cover all the synthetic patterns of isolated frequencies for any continuous system whose essential structure is fundamentally analogous to that for a composite single-degree-of-freedom model. Thus, a combined synthetic method for all such continuous systems is formulated, which may be regarded as an extension of the previous Southwell-Dunkerley methods.