The steered response power (SRP) method has been widely used in acoustic source localization because of its high accuracy and strong anti-noise ability. However, it has many local extrema, which affects the reliability of localization and results in high computational cost. In this paper, the spatial response of the SRP is defined to explain the SRP. Based on this, the formation mechanism of local extrema is analyzed, that is, the local extrema are related to the coherence of the generalized cross-correlation involved in the accumulation. The coherence can be evaluated by a coherence factor constructed from a statistical point of view. The SRP with coherence constraint is proposed, which is a simple and very effective method to suppress local extrema. Compared with the traditional SRP, the localization results of the simulation and actual data show that the proposed method can effectively suppress the local extrema without the loss of the localization accuracy of the traditional SRP method. [ABSTRACT FROM AUTHOR]