A phage display library of variable heavy domain (VHH or VH) fragments (sdAb fragments) derived from the antibody repertoire of a non-immunized llama is disclosed. The sdAb fragments of the library are characterized by the absence of cysteine residues in complementarity determining regions (CDRs) and a very low presence of residues of glutamic acid, arginine and glycine at positions 44, 45 and 47, respectively, of the VL interface of the variable heavy domain VHH. The large size of the library (in the order of 109) makes it a source of antigen-binding fragments having high affinity to almost any antigen of interest. The library is preferably generated using a modified fd-tet phage growing in plaques in the absence of a tetracycline.