Using Hamilton’s monotonicity formula for the Yang-Mills flow considered in R. S. Hamilton [Commun. Anal. Geom. 1, No. 1, 127–137 (1993; Zbl 0779.58037)], the author proves that a sequence of blow-ups of a rapidly forming singularity will converge, modulo the gauge group, to a non-trivial homothetically shrinking soliton, The last section contains explicit examples of such solitons in the case of trivial bundles over \(\mathbb R^n\) for \(5\leq n\leq9\).