  An essential problem in the design of holographic algorithms is to decide
whether the required signatures can be realized by matchgates under a suitable
basis transformation (SRP). For holographic algorithms on domain size 2, [1, 2,
4, 5] have built a systematical theory. In this paper, we reduce SRP on domain
size k>2 to SRP on domain size 2 for holographic algorithms on bases of rank 2.
Furthermore, we generalize the collapse theorem of [3] to domain size k>2.
