It is well known that in a free group , one has $\left|\right|{\chi }_E{\left|\right|}_{M_{cb}A\left(\right)}\le 2$, where E is the set of all the generators. We show that the (completely) bounded multiplier norm of any set satisfying the Leinert condition depends only on its cardinality. Consequently, based on a result of Wysoczański, we obtain a formula for $\left|\right|{\chi }_E{\left|\right|}_{M_{cb}A\left(\right)}$.