  Higher order necessary conditions for a minimizer of an optimal control
problem are generally obtained for systems whose dynamics is continuously
differentiable in the state variable. Here, by making use of the notion of
set-valued Lie bracket we obtain a Goh-type condition for a control affine
system with Lipschitz continuous dynamics and unbounded controls. In order to
manage the simultaneous lack of smoothness of the adjoint equation and of the
Lie bracket-like variations we make use of the notion of Quasi Differential
Quotient. We conclude the paper with a worked out example where the established
higher order condition is capable to rule out the optimality of a control
verifying the standard maximum principle.
