The present invention relates to a variant of Terminal deoxynucleotidyl Transferase (TdT) which (i) comprises the amino acid sequence as set forth in SEQ ID Nº 2 or a functionally equivalent sequence, with at least an amino acid substitution at position corresponding to residue C302 or functionally equivalent residue, wherein the position is numbered by reference to the amino acid sequence set forth in SEQ ID Nº 1, (ii) is able to synthesize a nucleic acid fragment without template and (iii) is able to incorporate a modified nucleotide into the nucleic fragment.