An unprecedented conversion of terminal alkynes into N-sulfonimidamides (amidines) is reported by a silver-catalyzed, one-pot, four-component reaction with TMSN3, sodium sulfinate, and sulfonyl azide. The reaction scope includes both aromatic and aliphatic alkynes. A possible cascade reaction mechanism, consisting of alkyne hydroazidation, sulfonyl radical addition, 1,3-dipolar cycloaddition by TMSN3, and retro-1,3-dipolar cycloaddition, is proposed. TMSN3 is found to play an essential role in each step of the reaction.