We point out that, if one accepts the validity of quantum mechanics, the Bell parameter for the polarization state of two photons can be measured in a simpler way than by the standard procedure [Clauser, Horne, Shimony, and Holt, Phys. Rev. Lett. 23,
880 (1969)]. The proposed method requires only two measurements with parallel linear-polarizer settings for Alice and Bob at 0 and 45 degrees, and yields a significantly smaller statistical error for a large Bell parameter.
