Some years ago a manuscript map from the third decade of the 16th century was found. Once its authenticity had been verified, it was presented to the academic world as the first representation of the western hemisphere, after its geography had become known, following the memorable exploratory journey of Fernando de Magallanes between 1519 and 1522. In the article, observations are made about the representation of the southernmost part of the New World (Strait of Magellan) in the map; and the differences between this and other maps known by this time are evaluated. Moreover, some lesser-known toponyms are pointed out, among them the name Land of Vespucci for one part of the discovered southernmost interoceanic channel. The denomination and its presumed origin are discussed, adding a different explanatory hypothesis for this curious and ephemeral name.