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We propose a different and direct test of Mach's principle, viz., to observe the spatial anisotropy of the transverse Doppler effect caused by the inertial motion of the photon.  From the almost perfect agreement of the results of our calculation with the observed data of Ives and Stilwell, we may draw two conclusions:  (1)  the conclusion of Ives and Stilwell that the transverse Doppler effect shows no directional effect is unfounded, and there does exist a spatial anistropy of this effect;  (2)  the inertial properties of the photon are determined by the structure of the whole universe, in agreement with the Mach's principle.  We propose that the IS experiment should be repeated with more precision, and we give a set of predictions of such an experiment.