Affine invariant point-set matching is an important issue in computer vision and pattern recognition. Using reference points derived from the convex hull of the point-set is an existing idea to solve this problem. However, how to choose proper and enough reference points for extracting affine invariant and powerful discriminative descriptors is an open problem. In this paper, a novel method termed convex hull bisection (CHB) is proposed for affine invariant point-set matching. In CHB, for each point in the point-set, two reference points are derived by bisecting the convex hull using the line connecting the point and the centroid of the convex hull. The resulting reference points and other reference points, such as the centroid point of the convex hull and the mean point of the point-set, are utilised to yield an 11-dimensional affine invariant feature vector associated with any point within the point-set. The obtained point based descriptors are used for point-set matching. The proposed method works well even in the case that reference points are overlapping or collinear, which overcomes the limitations of the existing convex hull based methods. The effectiveness of the proposed method is validated by an extensive experimental investigation.