A soft wheat flour containing bran, wherein the bran has a total fibre content comprised between 20 and 30% and a protein content comprised between 12.0 and 18.0% (% in weight of the total weight of the bran); such flour preferably has a bran content comprised between 5 and 30% and is produced by a process which comprises the process phases of a) subjecting soft wheat caryopses (101) to successive process phases involving abrasion in order to substantially remove the bran coating, thereby obtaining various bran fractions, the latter of which (D) originates from the removal of the aleurone, nucellar and testa layers; b) adding the latter bran fraction (D) to a soft wheat flour (F) substantially free of bran in a quantity such as to obtain a flour (C) containing from 5 to 30% of the total mixture weight of bran fraction (D); the invention furthermore refers to a soft wheat flour bakery product containing bran, wherein the bran has a total fibre content comprised between 20 and 30% and a protein content comprised between 12.0 and 18.0% (% in weight of the total weight of the bran), as well as to the use of a soft wheat bran fraction essentially containing the layers of the starting caryopses (101) consisting of the aleurone (105), nucellar (104) and testa (103) layers in the production of whole grain bakery products.