To provide a low-cost method for brazing an aluminum lap joint which is excellent in working easiness in the air while requiring no flux.

Aluminum thin clad sheet materials are previously inserted into the lap boundaries of several aluminum base materials. The aluminum base materials are brazed and hot-rolled to produce an aluminum alloy clad plate. In the production, the aluminum thin clad sheet materials 3 are consisting of three or five layers. The layer below the surface material is consisting of a brazing filler metal whose melting point is ≤600°C. Mg of 0.1 to 6% and possibly Bi of 0.01 to 1% are added to either one or more constitutional members. The whole of the clad members is heated to the liquidus temperature of the brazing filler metal or higher and to a range where the lowest value of the solidus temperature of each member is not exceeded while they are closely adhered under pressure. In this way, the plural aluminum base materials are brazed. After that, a rolling is performed thereto.