A catheter assembly (10) comprising: a catheter adapter (14) having a proximal end (22), a distal end (32) and a lumen (16) extending between the proximal end (22) and the distal end (32); a connection (50) arranged in the catheter adapter (14), the opening of the connection (50) in the lumen; and a valve (70) disposed within the lumen (16), the valve (70) which includes a flexible tube part (78) and a single-way valve part (76), a part of the part ( 78) flexible tube covering an opening between the connection (50) and the lumen (16), the one-way valve part (76) that limits the fluid flowing through the valve (70) to flow in a distal direction, the tube part (78) further comprising a substantially cylindrical shape, the one-way valve part (76) further comprising a duckbill valve, the valve part (76) being arranged a single track at the proximal end (22) of the valve (70), in which the one-way valve portion (76) is configured to withstand at least one average blood pressure in a proximal direction, characterized in that the catheter adapter is configured to force the fluid received through the connection to the proximal side to the valve.Un conjunto (10) de catéter que comprende: un adaptador (14) de catéter que tiene un extremo (22) proximal, un extremo (32) distal y un lumen (16) que se extiende entre el extremo (22) proximal y el extremo (32) distal; una conexión (50) dispuesta en el adaptador (14) de catéter, la abertura de la conexión (50) en el lumen; y una válvula (70) dispuesta en el interior del lumen (16), la válvula (70) que incluye una parte (78) de tubo flexible y una parte (76) de válvula de una sola vía, una parte de la parte (78) de tubo flexible que cubre una abertura entre la conexión (50) y el lumen (16), la parte (76) de válvula de una sola vía que limita el fluido que fluye a través de la válvula (70) para fluir en una dirección distal, la parte (78) de tubo que comprende además una forma sustancialmente cilíndrica, la parte (76) de válvula de un