 Nyorai kuenderera mberi kwechikamu chino - Ane vanhu vanodarika mazana matatu mungarava yake, Riou akabva kuSpithead musi wa 8 Gunyana 1789, uye akafamba rwendo rwusina zviitiko kuenda kuCape of Good Hope kwaakatakura zvipfuyo nezvirimwa zvakawanda. Ari paCape, Riou akasangana naLieutenant William Bligh, uyo akanga afamba nechikepe naRiou parwendo rwechitatu rwaCook panguva iyo Bligh akanga ari mutyairi mukuru weResolution. Bligh akanga asvika kuCape achibva kuTimor, kwaakanga asvika pashure perwendo rwemakiromita 3.618 ari muchikepe chakavhurika pashure pokupandukaari mungarava yake,. Pashure pokupedzisa kugoverwazve kwake, Riou akasimuka kubva kuCape pakati paDecember, ndokutora Westerlies, akatanga chikamu chechipiri cherwendo rwake kuenda kuNew South Wales. PaKrisimasi manheru, mazuva gumi nemaviri abva kuCape, iceberg guru rakaonekwa, uye Riou akasarudza kushandisa chando chacho kuti awedzere mvura yake yakachena yakanga yava kupera nokukurumidza nemhaka yokuda kuwanisa miti nemhuka dzaakanga achitakura. 