Abstract: In the early modal synthesis techniques, the main cause of computation error comes from the truncation of higher order natural vibration modes. In reference[1]~[4]it is revealed from various respects that the residual flexibility mode or attachment mode could be used to compensate the above mentioned truncation error. Based on the conclusions of [1]-[ 4], two kinds of new free boundary synthesis techniques have been developed. The first kind is presented in [3] and [4],in which the displacements of substructures are represented by linear combination of the free boundary modes and the residual flexibility modes. The second kind is presented in[2],in which the free boundary modes and the attachment modes are used together to represent the displacements of substructures. In this papet it is pointed out that the two kinds of techniques are equivalent to each other. The equivalence lies in the fact that the residual flexibility modes and the attachment modes could be replaced by each other. The theoretical proof is given to show that this replacement has no effect upon the final synthesis results. Besides, a more general conclusion is drawn. At the end of the paper, a numerical example is given.