This article aims to reveal what the concept of untranslatability is, what its conceptual and theoretical implications are, and how important postmodern translation approaches are, as holding a dominant position in the translation history of the millennium in terms of translation practice. In this article, in the light of Derrida’s deconstructionist/deconstructionist translation approach, which is the representative of the postmodern/poststructuralist discourse that determines today's translation theories, the idea of the indeterminacy of meaning and therefore the (im)possibilities of translation are discussed. For postmodern discourse, which emphasizes uncertainty/indefiniteness, difference/otherness and pluralism in every sense, the content in the Babylonian myth and the theme of languages being confounded emerge as a privileged site; as of yet, Babylon is an extension of both the realisability and destructibility of human/inter-communal communication and cultural exchange as well as a location that reveals the antagonistic nature of relations between texts, languages, traditions and cultures. Translation, like postmodern discourse, is faced with this antagonistic situation of "in-betweenness” and indeterminacy, thereby mediating the meaning between the source text and the target text so that one can recognize the other. Translation is always a “hybrid” by character and both translation and postmodernism produce discourse on the instability and inscrutability of signification in language and therefore of translation. In their discourses, the emphasis is placed on the intertextual context and it is underlined that the translated texts, which are claimed to always carry the traces of other texts and contexts, are actually autonomous formations. Translation has thus come to be conceptualized within the contemporary postmodern discourse as a rewriting, not as a reproduction of the "original. According to this situation, which means reading the texts from new perspectives, as predicted by the Derridean deconstruction strategy, there emerges a state of infinity of meaning and new layers of meaning are constantly appearing. Every effort to resolve the impasse in the transfer of the emerging layers of meaning also corresponds to a situation of untranslatability. In this study, which aims to illuminate the place of the concept of untranslatability in postmodern discourse, the concept of postmodernism is firstly discussed and then the effect of postmodern discourse on translation is tried to be determined. At the end of the study, it is revealed that the concept of untranslatability is in close relationship with the postmodern discourse, which reveals that the meaning is postponed forever, that it never remains fixed, and that it is redefined and reconstructed in each reading according to different political and cognitive backgrounds.