In　an　arbitrated　signature　scheme,　all　communications　involve　a　so　called　arbitrator　who　has　access　to　the　contents　of　the　messages.　The　security　of　most　arbitrated　signature　schemes　depends　heavily　on　the　trustworthiness　of　the　arbitrators.　In　this　paper　we　show　how　to　construct　an　arbitrated　quantum　signature　protocol　of　classical　messages　with　an　untrusted　arbitrator.　Its　security　is　analyzed　and　it　is　proved　to　be　secure　even　if　the　arbitrator　is　compromised.　In　addition,　the　proposed　protocol　does　not　require　a　direct　quantum　link　between　any　two　communicating　users,　which　is　an　appealing　advantage　in　the　implementation　of　a　practical　quantum　distributed　communication　network.