The parameter K in the quasi-relativistic INDO (QR-INDO) relation h(iAjB)(core) = 1/2 K S-ij (beta(i)(A) + beta(j)(B)) was optimized by applying the QR-INDO method to the optimization of the geometries and calculation of vibrational wavenumbers of 36 molecules of the XY(4) type with X = C, Si, Ti, Ge, Zr, Sn, Hf and Pb, and Y = H, F, Cl, Br and I. The calculations were performed for 10 values of K uniformly spaced across the region of 1.1 to 2.0. The optimum value with which the best fit of the bond lengths and vibrational frequencies was achieved was K = 1.5. This is very close to the value of 1.4 recommended in the literature. The study was performed using recent tabulated gas-phase data. The application of the variable scaling approximation approach was found generally unsuitable.