In view of the excellent copper(ii) and 64-copper(ii) complexation of a TE1PA ligand, a monopicolinate cyclam, in both aqueous medium and in vivo, we looked for a way to make it bifunctional, while maintaining its chelating properties. Overcoming the already known drawback of grafting via its carboxyl group, which is essential to the overall properties of the ligand, a TE1PA bifunctional derivative bearing an additional isothiocyanate coupling function on a carbon atom of the macrocyclic ring was synthesized. This led to an architecture that is comparable to that of other commercially available bifunctional copper(ii) chelators such as p-SCN-Bn-DOTA already used in clinical trials for 64Cu-immuno-PET imaging. The C-functionalization of TE1PA on one carbon atom in the β-N position of the cyclam backbone was successfully achieved by adapting our patented methodology to the huge challenge, allowing the regiospecific mono-N-functionalization of the unsymmetrical ligand. The obtained ligand p-SCN-Bn-TE1PA was coupled to a 9E7.4 murine antibody (mAb), an IgG2a anti CD-138 for multiple myeloma (MM) targeting. The conjugation efficiency was assessed by looking at the 64Cu radiolabeling and the radiopharmaceutical 64Cu-9E7.4-p-SCN-Bn-TE1PA immunoreactivity, and in particular by comparing with 9E7.4-p-SCN-Bn-NOTA and 9E7.4-p-SCN-Bn-DOTA obtained from commercial and presumably highly efficient chelators NOTA and DOTA, respectively. The results are quite clear, showing that p-SCN-Bn-TE1PA has a coupling rate 5 times higher and an immunoreactivity 1.5 to 2 times greater than those of its two competitors. p-SCN-Bn-TE1PA also outperforms TE1PA conjugated via its carboxylic function on the same antibody. The first 64Cu-immuno-PET preclinical study in a syngeneic model of MM was performed, confirming the good in vivo properties of 64Cu-9E7.4-p-SCN-Bn-TE1PA for PET imaging, considering the high clearance even after 24 h and the particularly important tumor-to-liver ratio that was increasing at 48 h.