  The Diffuse Interstellar Bands (DIBs) are absorption features seen in the
spectra of astronomical objects, that arise in the interstellar medium. Today
more than 500 DIBs have been observed mostly in the optical and near-infrared
wavelengths. The origin of the DIBs are unclear; only ionized
buckminsterfullerene C$_{60}^+$ has been identified as a viable candidate for
two strong and three weaker DIBs. In this study, we investigate the
correlations between the strengths of the two strongest C$_{60}^+$ DIBs as well
as their environmental behaviour. Therefore, we analysed measurements of the
strengths of the two C$_{60}^+$ DIBs at 9577 and 9633 $\r{A}$ for 26 lines of
sight. We used two different methods, including Monte Carlo simulations, to
study their correlations and the influence of measurement errors on the
correlation coefficients. Furthermore, we examined how the strength of the
C$_{60}^+$ DIBs changes as a result of different environmental conditions, as
measured by the concentration of H/H$_2$ and the strength of the ambient UV
radiation. In contrast to results recently reported by Galazutdinov et al.
(2021), we find a high correlation between the strengths of the C$_{60}^+$
DIBs. We also discovered that the behaviour of the correlated C$_{60}^+$ bands
is quite distinct from other DIBs at 5780, 5797 and 6203 $\r{A}$ in different
environments.
