This paper proposes a new global scan matching algorithm using the CIF descriptors and a geometric constraint between keypoints. The CIF descriptor was proposed in our previous work. It is a feature decriptor that is invariant against a congruence transformation. In our previous work, our method was able to perform robust local scan matching using CIF decriptors, but was apt to fail global scan mathching where a large map is used as the reference scan. In this paper, in order to resolve this problem, we propose to use a geometric constraint between keypoints in addtion to the CIF decriptors for the global scan mathching task. Our method can perform global scan matching in a cluttered environment without using an initial alignment. Through experiment in real environment, we confirm the validity of our method by comparing the performance of our method and that of our previous method.