The use of soft rotor formula (SRF) for the level energies of $K = 2 \gamma$ -band for the shape transitional even $Z$ even $N$ nuclei in the medium mass region is illustrated. With proper treatment, we obtained positive values of the moment of inertia and softness parameter, as opposed to negative values reported in literature. The moments of inertia of the $\gamma$-band are almost equal to the ground state band values. The systematic dependence of the softness parameter on energy ratio $R_{4/2}$ is studied. The effect of the odd–even spin staggering on these parameters is studied in detail. In deformed nuclei, the same parameters for odd and even spin members yield fair energy values.