Most of the previous relations1–3for the calculation of vibrational constant of diatomic molecules are electronegativity dependent. Electronegativity (X) is a complex quantity containing an atomic term depending on the charge and hybridization of the atom, and a molecular term depending on the length and the nature of the bonds in the molecule and as such it is not as precise as the bond length reor the reduced mass μ of the molecule. Thus the formule dependent on the electronegativity are expected to yield divergent results. Though there is a relation given by Varshni and Guggenheimer4which is free from electronegativity but the drawback is that it depends on too many quantities and also contains two empirical constants. Therefore it was thought to propose a new relation free from electronegativity, containing a single constant A, depending only on reand μ.