Abstract: The method in Ref.[1, 2] is derived basing upon complete measured modes, hence its derivation is unreasonable to uncomplete measured modes. In present paper the method is extended to uncomplete measured modes. which occur often in engineering. The paper describes. The paper describes the uniqueness of mass and stiffness matrices, M and K, of modified model obtained by simplest matrix perturbation method based solely on orthogonality conditions of mass and stiffness matrices. However such M and K matrices together with the measured normal mode shapes and natural frequencies could not satisfy the free vibration eigenequation. To overcome this drawback, either M or K is modified again by the optimal fitting method to be fit for the eigenequation.Implementation of present method is simple, since no trial-error and iterative processes are involved. Numerical examples show that accuracy of the method is good.