Objective/context: This article constructs a concept of memory as an open story in a domain of political reflection. It analyses the exercises of official memory-building found in reports such as the one written by the Historical Memory Documentary Centre (CNMH) establishing their paradoxical function with respect to social order and the victims. The argument is based on a claim regarding the impossibility of an absolute or totalizing closure of the political meaning of any narrative resulting from such reports. Methodology: The study was based on a poststructuralist theoretical perspective, with some conceptual corrections of the materialist paradigm and in consideration of the fieldwork involving the victims of the Colombian armed conflict in previous studies. We particularly emphasize the testimony of one of the victims interviewed in one of these previous works. Conclusions: The paper concludes that memory must constitute an open story that specifies a political and discursive interaction with the irrepresentable traumas linked to society's historical foundation. Originality: Theoretical analyses of memory exercises usually exalt the role of memory narratives in overcoming violent events or defending a search for an alternative truth from the one produced institutionally. In this article, we highlight the incommensurability of the conflict and criticize the idea of memory narratives with a closed and stable symbolization. We set out the effects of the memory narratives on a political level in which the irrepresentable traumas that reflect unreconciled victims are at stake. © 2019 Universidad de los Andes, Bogota Colombia. All rights reserved.