  We report triangular auto-B\"acklund transformations for the solutions of a
fifth-order evolution equation, which is a constraint for an invariance
condition of the Kaup-Kupershmidt equation derived by E. G. Reyes in his paper
titled "Nonlocal symmetries and the Kaup-Kupershmidt equation" [{\it J. Math.
Phys.} {\bf 46}, 073507, 19 pp., 2005]. These auto-B\"acklund transformations
can then be applied to generate solutions of the Kaup-Kupershmidt equation. We
show that triangular auto-B\"acklund transformations result from a systematic
multipotentialisation of the Kupershmidt equation.
