An agent is said to be partially honest if he or she weakly prefers an outcome at a strategy profile with his truthful strategy than an outcome at a strategy profile with his false strategy, then this player must prefer strictly the \true" strategy profille to the \false" strategy profile. In this paper we consider an exchange economy with single peaked preferences. With many agents (n ≥3), if there exists at least one partially honest agent, we prove that any solution of the problem of fair division satisfying unanimity is Nash implementable.