Method of production of a heat exchanger with at least two fluid circuits each one comprising channels, characterized in that involves the following steps: a/ production of at least two elementary modules of the exchanger (1.1, 1.2, 1.3, etc.), the production of each elementary module involving the following steps: i/ production of one or more elements of one of the two fluid circuits, the so-called first circuit, each element of the first circuit comprising at least one metal plate comprising first grooves forming at least one portion of the channels of the first circuit; ii/ production of one or more elements of at least one other fluid circuit, the so-called second circuit, each element of the second circuit comprising at least one metal plate comprising second grooves forming at least one portion of the channels of the second circuit; iii/ stacking of the metal plates of the elements of the first and second circuits in order to form their channels (2, 3); iv/ assembling by diffusion bonding of the element or elements of the first circuit and the element or elements of the second circuit, stacked one on the other; b/ modification of at least one of the elementary modules involving a reduction of the width of at least one of the borders and/or of the thickness of at least one of the anvils of at least one of the modules and optionally an opening of the channels (2, 3) of the first circuit and/or of the second circuit to the outside; c/ edge to edge positioning of the elementary modules (1.1, 1.2, 1.3, etc.), at least one of which is reduced, along one of their longitudinal edges or one of their lateral edges; d/ assembling of the interfaces between the edge to edge elementary modules in order to obtain the exchanger in one-piece form. a/ production of at least two elementary modules of the exchanger (1.1, 1.2, 1.3, etc.), the production of each elementary module involving the following steps: i/ production of one or more elements of one of the two fluid circuits, the so-called first circuit, each element of the first circuit comprising at least one metal plate comprising first grooves forming at least one portion of the channels of the first circuit; ii/ production of one or more elements of at least one other fluid circuit, the so-called second circuit, each element of the second circuit comprising at least one metal plate comprising second grooves forming at least one portion of the channels of the second circuit; iii/ stacking of the metal plates of the elements of the first and second circuits in order to form their channels (2, 3); iv/ assembling by diffusion bonding of the element or elements of the first circuit and the element or elements of the second circuit, stacked one on the other; i/ production of one or more elements of one of the two fluid circuits, the so-called first circuit, each element of the first circuit comprising at least one metal plate comprising first grooves forming at least one portion of the channels of the first circuit; ii/ production of one or more elements of at least one other fluid circuit, the so-called second circuit, each element of the second circuit comprising at least one metal plate comprising second grooves forming at least one portion of the channels of the second circuit; iii/ stacking of the metal plates of the elements of the first and second circuits in order to form their channels (2, 3); iv/ assembling by diffusion bonding of the element or elements of the first circuit and the element or elements of the second circuit, stacked one on the other; b/ modification of at least one of the elementary modules involving a reduction of the width of at least one of the borders and/or of the thickness of at least one of the anvils of at least one of the modules and optionally an opening of the channels (2, 3) of the first circuit and/or of the second circuit to the outside; c/ edge to edge positioning of the elementary modules (1.1, 1.2, 1.3, etc.), at least one of which is reduced, along one of their longitudinal edges or one of their lateral edges; d/ assembling of the interfaces between the edge to edge elementary modules in order to obtain the exchanger in one-piece form.