Fractionally spaced super‐exponential (FSSE) algorithm has the disadvantage of computational complexity since it exploits high‐order statistics explicitly. The authors propose a dimension degradation technique for FSSE when it is applied to the equalisation of a sparse channel in accordance with the relationship between the coefficients of the cross fourth‐order cumulant (CFOC) in FSSE and the channel impulse response. They implement partial updating on the prominent coefficients of the CFOC with all the small coefficients remaining unchanged. The computational complexity of the modified FSSE reduces significantly with an acceptable performance loss, and its performance is validated via numerical simulations.