  As a natural generalization of line graphs, Hoffman line graphs were defined
by Woo and Neumaier. Especially, Hoffman line graphs are closely related to the
smallest eigenvalue of graphs, and the uniqueness of strict covers of a Hoffman
line graph plays a key role in such a study. In this paper, we prove a theorem
for the uniqueness of strict covers under a condition which can be checked in
finite time. Our result gives a generalization and a short proof for the main
part of [Ars Math.~Contemp. \textbf{1} (2008) 81--98].
