A conjugate addition reaction between an α,β-unsaturated ketone compound and a carbamate compound is carried out to synthesize a β-aminoketone, a salt or a hydrate salt of a transition metal of Groups 7 to 11 of the Periodic Table of Elements being present in the reaction system as the catalyst. The novel method and the catalyst are capable of synthesizing the β-aminoketone by the Aza-Michael reaction with high yield and efficiency.