A method for cleaning fabrics or hard surfaces, said method comprising contacting a fabric or hard surface in need of cleaning with an oxygen bleaching agent, preferably selected from the group consisting of hydrogen peroxide, perborate salt, percarbonate salt, and mixtures thereof, a bleach activator and/or organic percarboxylic acid, and a transition-metal bleach catalyst, wherein said transition-metal bleach catalyst comprises a complex of a transition metal selected from the group consisting of Mn(II), Mn(III), Mn(IV), Mn(V), Fe(II), Fe(III), Fe(IV), Co(I), Co(II), Co(III), Ni(I), Ni(II), Ni(III), Cu(I), Cu(II), Cu(III), Cr(II), Cr(III), Cr(IV), Cr(V), Cr(VI), V(III), V(IV), V(V), Mo(IV), Mo(V), Mo(VI), W(IV), W(V), W(VI), Pd(II), Ru(II), Ru(III), and Ru(IV), preferably Mn(II), Mn(III), Mn(IV), Fe(II), Fe(III), Cr(II), Cr(III), Cr(IV), Cr(V), and Cr(VI), preferably Mn, Fe and Cr in the (II) or (III) state, coordinated with a macropolycyclic rigid ligand, having at least 4 donor atoms, at least two of which are bridgehead donor atoms.