To calculate the IR band shapes of CH₄ in dense gases and liquids, a model is developed that takes into account both the collisional rotational perturbations and the intramolecular Coriolis coupling. The model is used to analyze the dependence of the V₂ and V₄ band shapes on the molecular rotational relaxation rate τ^-1. The calculations performed make allowance for the Coriolis interaction of the V₂, V₃, and V₄ bands. The strong-collision model is used to treat the rotational relaxation. The simulations reveal a significant distinction in transformations of the V₂ and V₄ band shapes on increasing τ^-1. As τ^-1 increases, the V₄ band begins to narrow, whereas the "forbidden" V₂ band broadens; its shape drastically differs from those typical for the "allowed" vibrational bands with a similar rotational structure.