The present invention relates to a modified antibody comprising a heavy chain and a light chain, wherein the heavy chain or/and the light chain comprises one or more first recognition site(s) for the transglutaminase from Kutzneria albida (KalbTG) or a functionally active variant thereof. The one or more first recognition site(s) are introduced at one or more selected position(s) within the antibody's heavy chain and/or light chain. The invention further relates to one or more nucleic acids encoding the modified antibody according to the invention as well as a covalent conjugate comprising (i) the modified antibody according to the invention and (ii) one or more non-antibody moieties (payload(s)) covalently conjugated to the one or more first recognition site(s) either directly or via a first linker. In certain embodiments, the non-antibody moiety comprises a therapeutic entity and optionally a second linker. The present invention further relates to a method of covalently conjugating a modified antibody according to the invention to non-antibody moieties. In case the non-antibody moiety comprises a therapeutic entity, the present invention further relates to the conjugate of the modified antibody according to the invention and the therapeutic entity as pharmaceutical composition, for use as a medicament as well as for use in treating a disease.