In order to improve the efficiency of optimizing compilers, integration of register allocation and instruction scheduling has been extensively studied. One of the promising integration techniques is register allocation based on register-reuse chains. However, the generation of register-reuse chains in the previous approach was not completely systematic and consequently it creates unnecessarily dependencies that restrict instruction scheduling. This paper proposes a new register allocation technique based on a systematic generation of register-reuse chains. The first phase of the proposed technique is to generate register-reuse chains that are optimal in the sense that no additional dependencies are created. Thus, register allocation can be done without restricting instruction scheduling. For the case when the optimal register-reuse chains require more than available registers, the second phase reduces the number of required registers by merging the register-reuse chains. Chain merging always generates additional dependencies and consequently enforces the execution order of instructions. A heuristic is developed for the second phase in order to reduce additional dependencies created by merging chains. For matrix multiplication program, the number of registers resulting from the first phase is small enough to fit into available registers for most basic blocks. In addition, it is shown that the restriction to instruction scheduling is reduced by the proposed merging heuristic of the second phase.