This paper is concerned with the problem of robust unbiased H∞ filtering for uncertain two-dimensional (2-D) systems described by the Fornasini-Marchesini local state-space second model. The parameter uncertainties are assumed to be norm-bounded in both the state and measurement equations. The concept of robust unbiased filtering is first introduced into uncertain 2-D systems. A necessary and sufficient condition for the existence of robust unbiased 2-D H∞ filters is derived based on the rank condition of the given system matrices. A method is then proposed for the design of robust unbiased H∞ filters for uncertain 2-D systems using a linear matrix inequality (LMI) technique. The main advantage of the proposed method is that it can be applied to unstable uncertain 2-D systems while existing robust 2-D H∞ filtering approaches only work for robust stable uncertain 2-D systems. An illustrative example is also provided and comparison with existing results is made.