The method is for separation of lignin from original black liquor (BLIN) having the following phases in sequence; a first precipitation phase (PR1) for precipitation of lignin by a first acidification of the original black liquor by adding a first acid or mixture of acids (G1a); followed by a second precipitation phase (PR2) for precipitation of lignin by a further acidification of the original black liquor by adding a second acid or mixture of acids (G1b). The first phase is implemented to lower the pH while avoiding any larger amount of precipitation, i.e. less than 2-5%, while the second phase is implemented in order to obtain the larger part of the precipitation. In total is 40-70% of the total lignin content of the original black liquor precipitated while the residual black liquor after precipitation is still strongly alkaline.