A method for brazing an aluminum alloy brazing sheet, comprising brazing an aluminum alloy brazing sheet in an inert gas atmosphere at a heating temperature in a range of from 560°C to 620°C without using a flux, wherein: the aluminum alloy brazing sheet comprises a core material and a brazing filler material disposed on at least one surface of the core material; the core material comprises an aluminum alloy having an Mg content of 2.0 mass% or less, including 0 mass%, with the remainder being Al and unavoidable impurities; the core material optionally comprises at least one selected from the following (f) to (k): (f) 2.5 mass% or less of Mn; (g) 1.2 mass% or less of Si; (h) 3.0 mass% or less of Cu; (i) 1.5 mass% or less of Fe; (j) one or more of 0.5 mass% or less of Ti, 0.5 mass% or less of Cr, and 0.5 mass% or less of Zr; and (k) 0.3 mass% or less of Li; the brazing filler material comprises an aluminum alloy comprising Si, Bi, and Mg with the remainder being Al and unavoidable impurities; the following relationships are satisfied: 3 ≤ C Si ≤ 13; 0.13 C Mg − 0.3 ≤ C Bi ≤ 0.58 C Mg 0.45; C Mg − b ≥ 0.1; and 0.2 ≤ C Mg ≤ 0.9, wherein C Si is an Si content of the brazing filler material in mass%, C Bi is a Bi content of the brazing filler material in mass%, C Mg-b is an Mg content of the brazing filler material in mass%, C Mg-c is an Mg content of the core material in mass% and C Mg is defined as C Mg =C Mg-b +C Mg-c /2; and the brazing filler material optionally comprises at least one selected from the following (a) to (e): (a) one or more of 2.0 mass% or less of Mn, 0.3 mass% or less of Ti, 0.3 mass% or less of Cr, and 0.3 mass% or less of Zr; (b) 5.0 mass% or less of Zn; (c) one or more of 0.10 mass% or less of Sr, 0.050 mass% or less of Na, and 0.5 mass% or less of Sb; (d) 1.0 mass% or less of one or more rare-earth elements; and (e) 0.3 mass% or less of Li. the aluminum alloy brazing sheet comprises a core material and a brazing filler material disposed on at least one surface of the core material; the core material comprises an aluminum alloy having an Mg content of 2.0 mass% or less, including 0 mass%, with the remainder being Al and unavoidable impurities; the core material optionally comprises at least one selected from the following (f) to (k): (f) 2.5 mass% or less of Mn; (g) 1.2 mass% or less of Si; (h) 3.0 mass% or less of Cu; (i) 1.5 mass% or less of Fe; (j) one or more of 0.5 mass% or less of Ti, 0.5 mass% or less of Cr, and 0.5 mass% or less of Zr; and (k) 0.3 mass% or less of Li; (f) 2.5 mass% or less of Mn; (g) 1.2 mass% or less of Si; (h) 3.0 mass% or less of Cu; (i) 1.5 mass% or less of Fe; (j) one or more of 0.5 mass% or less of Ti, 0.5 mass% or less of Cr, and 0.5 mass% or less of Zr; and (k) 0.3 mass% or less of Li; the brazing filler material comprises an aluminum alloy comprising Si, Bi, and Mg with the remainder being Al and unavoidable impurities; the following relationships are satisfied: 3 ≤ C Si ≤ 13; 0.13 C Mg − 0.3 ≤ C Bi ≤ 0.58 C Mg 0.45; C Mg − b ≥ 0.1; and 0.2 ≤ C Mg ≤ 0.9, wherein C Si is an Si content of the brazing filler material in mass%, C Bi is a Bi content of the brazing filler material in mass%, C Mg-b is an Mg content of the brazing filler material in mass%, C Mg-c is an Mg content of the core material in mass% and C Mg is defined as C Mg =C Mg-b +C Mg-c /2; and the brazing filler material optionally comprises at least one selected from the following (a) to (e): (a) one or more of 2.0 mass% or less of Mn, 0.3 mass% or less of Ti, 0.3 mass% or less of Cr, and 0.3 mass% or less of Zr; (b) 5.0 mass% or less of Zn; (c) one or more of 0.10 mass% or less of Sr, 0.050 mass% or less of Na, and 0.5 mass% or less of Sb; (d) 1.0 mass% or less of one or more rare-earth elements; and (e) 0.3 mass% or less of Li. (a) one or more of 2.0 mass% or less of Mn, 0.3 mass% or less of Ti, 0.3 mass% or less of Cr, and 0.3 mass% or less of Zr; (b) 5.0 mass% or less of Zn; (c) one or more of 0.10 mass% or less of Sr, 0.050 mass% or less of Na, and 0.5 mass% or less of Sb; (d) 1.0 mass% or less of one or more rare-earth elements; and (e) 0.3 mass% or less of Li.