  We present a short and self-contained proof of the following result: a random
time is an honest time that avoids all stopping times if and only if it
coincides with the (last) time of maximum of a nonnegative local martingale
with zero terminal value and no jumps while at its running supremum, where the
latter running supremum process is continuous. Illustrative examples involving
local martingales with discontinuous paths are provided.
