The invention pertains to a method for disinfecting a surface which is contaminated with microorganisms or which is suspected of being contaminated with microorganisms, the microorganism being one or more of Escherichia coli, Staphylococcus aureus, Pseuo!omonas aeruginosa, and Enterococcus hirae, comprising the step of contacting the surface with a disinfecting composition comprising: - 0.1-10 wt. % of one or more N-acylated amino acids or N- acylated peptides, or a salt thereof, - less than 0.1 wt. % of hydrogen peroxide, - 0.1-20 wt. % of one or more non-ethoxylated anionic surfactants, - 0.05-5 wt. % of a carboxylic acid, wherein the disinfecting composition has a pH in the range of 1-4.5 wherein the composition comprises less than 5 wt. % of ethoxylated anionic surfactant. The invention also pertains to a composition suitable for use in the method according to the invention. An advantage of the method and composition of the invention is that it provides excellent biocidal activity over a broad range of organisms using low concentrations of organic acids.