We propose a scalable method for implementing linear optics quantum computation using the "linked-state" approach. Our method avoids the two-dimensional spread of errors occurring in the preparation of the linked state. Consequently, a proof is given for the scalability of this modified linked-state model, and an exact expression for the efficiency of the method is obtained. Moreover, a considerable improvement in the efficiency, relative to the original linked-state method, is achieved. The proposed method is applicable to Nielsen's optical "cluster-state" approach as well.