A priori attitude information can improve the success rate and reliability of Global Navigation Satellite System (GNSS) multi-antennae attitude determination. However, a priori attitude information is nonlinear, and integrating a priori information into the objective function rigorously will increase the complexity of an ambiguity domain search, such as the Multivariate Constrained-Least-squares Ambiguity Decorrelation Adjustment (MC-LAMBDA) method. In this paper, a new method based on attitude domain search is presented to make use of the a priori attitude angle information with high efficiency. First, the a priori information of pitch and roll is integrated into the search process to derive the analytic search step for attitude angle, and the integer candidates are determined by traversal search in the three-dimensional attitude domain. Then, the objective function is parameterised with Euler angles, and a non-iterative approximate method is utilised to simplify the iterative computation in calculating objective function values. Experimental results reveal that compared to the MC-LAMBDA method, our new method has the same success rate and reliability, but higher efficiency in making use of a priori attitude information.