We introduce the concept of Convertible and Constrained Nucleic Acids (C2NAs). By means of the synthesis of a stereocontrolled N-propargyl dioxo-1,3,2-oxaza-phosphorinane as an internucleotidic linkage, the torsional angles α and β can adopt either the canonical (g-, t) set of values able to increase DNA duplex stability or the non-canonical (g+, t) set that stabilized the hairpin structure when installed within the loop moiety. With an appended propargyl function on the nitrogen atom of the six-membered ring, the copper catalysed Huisgen's cycloaddition (CuAAC click chemistry) allows for the introduction of new functionalities at any location on the nucleic acid chain while maintaining the properties brought by the geometrical constraint and the neutral internucleotidic linkage.