Existing Few-Shot Segmentation (FSS) approaches usually struggle with achieving high performance due to the challenge of effectively utilizing limited samples in the segmentation task. Upon reevaluating recent studies, a key observation is that the random selection of support images from training samples is not always the optimal. The random support selection scheme normally fails in the scenario where the query image and the support images selected exhibit significant differences. In this situation, the support images cannot provide the useful guidance for the segmentation task. Therefore, we argue that a similarity-based support selection scheme, which selects support images according to the similarity between the query image and candidate support images, is able to boost the performance of FSS networks. To this end, we introduce a Siamese Support Selection Network (SSSN) which can be end-to-end trained along with an FSS network. The SSSN automatically determines a set of support images by measuring the similarity between the query and candidate support images. To our knowledge, the idea of the similarity-based support selection has not been utilized for the FSS task. In addition, we leverage the joint utilization of a Convolutional Neural Network (CNN) and a Transformer network on top of a new feature fusion method that we design to further improve the segmentation performance. Experimental results show that the proposed approach outperforms its counterparts on three data sets for the FSS task. In particular, our SSSN is able to greatly boost the performance of an FSS network. We believe that the promising result should be due to the fact that the SSSN selects the top similar support images, which are useful for guiding the FSS task.