Lyapunov characterizations of output finite-time stability are presented for the system $x' = f (x), y = h(x)$ which is locally Lipschitz continuous out of the set $Y = {x ∈ R n : h(x) = 0}$ and continuous on $R^n$. The definitions are given in the form of $K$ and $KL$ functions. Necessary and sufficient conditions for output finite-time stability are given using Lyapunov functions. The theoretical results are supported by numerical examples.