In this paper, we present a new method for isolating real roots of a bivariate nonlinear system. It is a subdivision method based on analyzing the local geometrical properties of the given system. We propose the concept of opposite monotone system in a box and use it to determine the existence and the uniqueness of a simple real zero of the system in the box. We have implemented our method and the experiments show the effectivity and efficiency of our approach, especially for high degree sparse polynomial systems. This paper is an extended version of the ISSAC'19 conference paper (Cheng and Wen (2019))