Abstract: A connection for the junction of two tubes, through which a fluid under pressure flows, comprises a female element and a male element. The male element is adapted to be fitted axially in the female element and secured to the female element via a primary attachment member. The male and female elements dispose respectively of a female duct and a male duct, each of them opening on either side of the element in which it is located. Each of these ducts also comprises a first as well as a second extremity, these first extremities of the female duct and the male duct opening respectively on the flat surface of the female element and on the flat surface of the male element. The connection is manufactured in such a way that the flat surface of the female element and the flat surface of the male element are in flat contact.