The spectral angle mapper (SAM) has been widely used in multispectral and hyperspectral image analysis to measure spectral similarity between substance signatures for material identification. It has been shown that the SAM is essentially the Euclidean distance when the spectral angle is small. Most recently, a stochastic measure, called the spectral information divergence (SID), has been suggested to model the spectrum of a hyperspectral image pixel as a probability distribution, so that spectral variations among spectral bands can be captured more effectively in a stochastic manner. This paper develops a new hyperspectral spectral discrimination measure, which combines the SID and the SAM into a mixed measure. More specifically, let r and r′ denote two hyperspectral image pixel vectors with their corresponding spectra specified by s and s′. Then SAM(s,s′) measures the spectral angle between s and s′. Similarly, SID(s,s′) measures the information divergence between the probability distributions generated by s and s. The proposed new measure, referred to as the SID-SAM mixed measure, can be implemented in two versions, given by SID(s,s′)×tan(SAM(s,s′)) and SID(s,s′)×sin(SAM(s,s′)), where tan and sin are the usual trigonometric functions. The spectral discriminability of such a mixed measure is greatly enhanced by multiplying the spectral abilities of the two measures. In order to demonstrate its utility, a comparative study is conducted among the SID-SAM mixed measure, the SID, and the SAM. Our experimental results have shown that the discriminatory ability of the (SID,SAM) mixed measure can be a significant improvement over the SID and SAM.