A method for manufacturing a heat exchanger, comprising: assembling an object to be processed by disposing an inner fin within an interior of a hollow structure formed from at least two clad plates (200a, 200b) that each have a filler metal layer disposed on a side thereof that faces the interior of the hollow structure and contacts the inner fin; and heating the object to be processed in an inert-gas atmosphere to melt the filler metal layer and join the hollow structure to the inner fin and to join the at least two clad plates (200a, 200b) to each other along a contact part; wherein: the at least two clad plates (200a, 200b) each comprise the filler metal layer clad onto a core layer, the core layer is composed of an aluminum alloy that contains Mg: 0.40-1.0 mass%; the filler metal layer is composed of an aluminum alloy that contains Si: 4.0-13.0 mass%, and further contains one or two elements selected from the group consisting of Li: 0.0040-0.10 mass% and Bi: 0.01-0.30 mass%, the filler metal layer containing less than 0.10 mass% Mg; the inner fin is composed of an aluminum alloy that contains Si: 0.30-0.70 mass% and Mg: 0.35-0.80 mass%; and a flux that contains cesium (Cs) is applied to the contact part, and to the vicinity thereof, of the at least two clad plates (200a, 200b) prior to the brazing, wherein the flux melts during the heating step to break up oxide films on surfaces of the at least two clad plates (200a, 200b) along the contact part. assembling an object to be processed by disposing an inner fin within an interior of a hollow structure formed from at least two clad plates (200a, 200b) that each have a filler metal layer disposed on a side thereof that faces the interior of the hollow structure and contacts the inner fin; and heating the object to be processed in an inert-gas atmosphere to melt the filler metal layer and join the hollow structure to the inner fin and to join the at least two clad plates (200a, 200b) to each other along a contact part; wherein: the at least two clad plates (200a, 200b) each comprise the filler metal layer clad onto a core layer, the core layer is composed of an aluminum alloy that contains Mg: 0.40-1.0 mass%; the filler metal layer is composed of an aluminum alloy that contains Si: 4.0-13.0 mass%, and further contains one or two elements selected from the group consisting of Li: 0.0040-0.10 mass% and Bi: 0.01-0.30 mass%, the filler metal layer containing less than 0.10 mass% Mg; the inner fin is composed of an aluminum alloy that contains Si: 0.30-0.70 mass% and Mg: 0.35-0.80 mass%; and a flux that contains cesium (Cs) is applied to the contact part, and to the vicinity thereof, of the at least two clad plates (200a, 200b) prior to the brazing, wherein the flux melts during the heating step to break up oxide films on surfaces of the at least two clad plates (200a, 200b) along the contact part. the at least two clad plates (200a, 200b) each comprise the filler metal layer clad onto a core layer, the core layer is composed of an aluminum alloy that contains Mg: 0.40-1.0 mass%; the filler metal layer is composed of an aluminum alloy that contains Si: 4.0-13.0 mass%, and further contains one or two elements selected from the group consisting of Li: 0.0040-0.10 mass% and Bi: 0.01-0.30 mass%, the filler metal layer containing less than 0.10 mass% Mg; the inner fin is composed of an aluminum alloy that contains Si: 0.30-0.70 mass% and Mg: 0.35-0.80 mass%; and a flux that contains cesium (Cs) is applied to the contact part, and to the vicinity thereof, of the at least two clad plates (200a, 200b) prior to the brazing, wherein the flux melts during the heating step to break up oxide films on surfaces of the at least two clad plates (200a, 200b) along the contact part.