Fundamental bandgaps and Schottky barrier heights of strain-relaxed quaternary InxAlyGa1-x-yAs alloys with 0 < x < 0.35 and 0 < y < 0.30 were studied. The alloys were grown on GaAs substrates by molecular beam epitaxy. The lattice mismatch (up to 2.5%) and mismatch strain were accommodated by a compositionally-step-graded buffer. A residual compressive strain of less than 0.5% was determined by x-ray diffraction. Measured Schottky barrier heights v.s. bandgap deviate from the values predicted by the “common-anion” rule. This behavior is attributed to the compositional inhomogeneities and chemical reactivity of the air-exposed InAlGaAs surfaces.