The aim is to demonstrate the potential impact of changes in the value of the β parameter in the linear quadratic (LQ) model on the calculation of clinical relative biological effectiveness (RBE) values used for high linear energy transfer (LET) radiotherapy. The parameter RBE(min) is introduced into the LQ formulation to account for possible changes in the β radiosensitivity coefficient with changing LET. The model is used to fit fractionated data under two conditions, where RBE(min) = 1 and RBE(min) ≠ 1. Nonlinear regression and analysis of variance are used to test the hypothesis that the inclusion of a non-unity value of RBE(min) better predicts the total iso-effective dose required at low number of fractions for fast neutrons, carbon ions, π-meson and proton fractionation data obtained for various tissues from previous publications. For neutrons the assumption of RBE(min) ≠ 1 provided a better fit in 89% of the cases, whereas for carbon ions RBE(min) ≠ 1 provided a better fit only for normal tissue at the spread-out Bragg peak. The results provide evidence of the impact that variations in the β parameter may have when calculating clinically relevant RBE values, especially when using high doses per fraction (i.e. hypofractionation) of high-LET radiations.