We complied the optical, X-ray, and {gamma}-ray data for 54 Fermi blazars and studied the relationship between the broadband spectral index {alpha}_ox_ and {alpha}_x{gamma}_, as well as the relationship between the intrinsic composite spectral indices {alpha}_xox_ and {alpha}_{gamma}x{gamma}_ for this sample. The relationship between {alpha}_xox_ and {alpha}_{gamma}x{gamma}_ reveals that flat spectrum radio quasars and low-energy peaked BL Lacertae follow a continuous trend, which is consistent with previous results, whereas high-energy peaked BL Lacertae follow a separate distinct trend. Even so, a unified scheme is also revealed from {alpha}_xox_-{alpha}_{gamma}x{gamma}_ diagram when all three subclasses of blazars are considered.