Multimode fibers (MMF) are used in many applications from telecomunications to minimally invasive micro-endoscopic imaging. However, the numerous modes and their coupling make light-beam control and imaging a delicate task. To circumvent this difficulty, recent methods exploit priors about the transmission of the system, such as the so-called optical memory effect. Here, we quantitatively characterize a chromato-axial memory effect in step-index MMF, characterized through its slope $\delta z/\delta \lambda$ and its spectral and axial widths. We propose a theoretical model and numerical simulations in good agreement with experimental observations.