The present invention relates to methods and intermediates for chemical synthesis of polypeptides and proteins, and more particularly to methods and intermediates for chemically ligating a peptide fragment containing N-terminal N-methyl-cysteine (SEQ ID NO: 1) with another peptide fragment having C-terminal thioester to generate a β-(methylamino)-thioester intermediate that spontaneously rearranges to form an amide bond. Furthermore, the invention relates to methods of converting N-methyl-thiazolidine to N-methyl-cysteine (SEQ ID NO: 1) of polypeptides and proteins. The invention also relates to methods of synthesizing peptide-thioester from peptide-acid fluoride.