The exact reanalysis of a structure is time consuming and when repeated reanalyses are needed, it is often preferable to use an approximate Ritz technique. This approximate method consists in expressing the new frequency response function as a linear combination of vectors in a truncated modal basis. One notices that even though the convergence to the exact frequency response function is monotonic, it is generally irregular when the number of vectors introduced in the modal sub-basis increases. A solution to this consists of choosing the additional eigenvectors of the basis in such a way so as to give a best representation of the new frequency response function. This choice is not an easy task, particularly when the parametric modifications are very local and of large amplitudes. This article describes an original approximate reanalysis technique for accurately evaluating frequency response of a modified structure. It introduces new concepts for evaluating the static contribution of the neglected eigenvectors resulting in a set of additional vectors completing the original Ritz basis. This method will be appreciated by designers working on the optimization of a prototype. It can also be used during the iterations of a model updating procedure based on measured frequency response functions.