A brazing sheet material for CAB brazing without applying flux. The brazing sheet material including an aluminum core alloy layer provided with a first brazing clad layer material on one or both sides of the aluminum core layer and at least one second brazing clad layer material positioned between the aluminum core alloy layer and the first braze clad layer material. The second brazing clad layer material is an Al—Si alloy brazing material having 5% to 20% Si and 0.01% to 3% Mg, and the first brazing clad layer material is an Al—Si alloy brazing material having 2% to 14% Si and less than 0.4% Mg. Also disclosed is a brazed assembly manufactured in a brazing operation.