Calcium carbonate with high brightness is prepared by treating calcium carbonate and/or the milk of lime used for its preparation by reacting milk of lime with carbon dioxide and/or at least one of the calcium-containing preliminary products used for the preparation of the milk of lime before, during and/or after this reaction with a bleaching agent which comprises at least one compound of the formula (I): A[(CR.sup.1R.sup.2)SO.sub.pM.sub.(1/q)].sub.r (I) where the variables have the following meanings: TABLE-US-00001 A is NR.sup.3R.sup.4, NR.sup.3, N or OH; R.sup.1, R.sup.2, R.sup.3, R.sup.4 independently of one another, are hydrogen or an organic radical; M is ammonium or metal p is 2 or 3; q is the valency of M; and r is 1 when A = OH or NR.sup.3R.sup.4, is 2 when A = NR.sup.3 and is 3 when A = N; and where variables, if a mixture of compounds is used and/or r=2 or 3, are chosen independently of one another for each individual compound and/or for each [(CR.sup.1R.sup.2)SO.sub.pM.sub.(1/q)] group.