A heterodimer molecule, comprising a first polypeptide chain and a second polypeptide chain, wherein said first polypeptide chain comprises a first CH3 domain of an antibody heavy chain constant region, said second polypeptide chain comprises a second CH3 domain of an antibody heavy chain constant region, and comparing to a corresponding wild-type CH3 domain of a human antibody heavy chain constant region, said first CH3 domain and said second CH3 domain comprise amino acid mutations and said amino acid mutations consist of substitution mutations selected from the following groups: 1) said first CH3 domain: T366+K409+K392, said second CH3 domain: T366+L368+Y407+D399+F405; 2) said first CH3 domain: T366+K409, said second CH3 domain: T366+L368+Y407+F405; 3) said first CH3 domain: T366+K409+Y349, said second CH3 domain: T366+L368+Y407+F405+E357; and 4) said first CH3 domain: T366+K409+Y349+S354, said second CH3 domain: T366+L368+Y407+F405+E357; wherein said wild-type CH3 domain of the human antibody heavy chain constant region is a CH3 domain of a human IgG1 heavy chain constant region, wherein in said first CH3 domain: said amino acid mutation at T366 is T366W; said amino acid mutation at K409 is K409A; said amino acid mutation at K392 is K392D; said amino acid mutation at Y349 is Y349D; and said amino acid mutation at S354 is S354D; and wherein in said second CH3 domain: said amino acid mutation at T366 is T366S; said amino acid mutation at L368 is L368A and said amino acid mutation at Y407 is Y407V; or said amino acid mutation at L368 is L368G and said amino acid mutation at Y407 is Y407A; said amino acid mutation at D399 is D399S; said amino acid mutation at F405 is F405K; and said amino acid mutation at E357 is E357A; and wherein said amino acid is numbered according to the EU index of the KABAT numbering of the antibody Fc region. 1) said first CH3 domain: T366+K409+K392, said second CH3 domain: T366+L368+Y407+D399+F405; 2) said first CH3 domain: T366+K409, said second CH3 domain: T366+L368+Y407+F405; 3) said first CH3 domain: T366+K409+Y349, said second CH3 domain: T366+L368+Y407+F405+E357; and 4) said first CH3 domain: T366+K409+Y349+S354, said second CH3 domain: T366+L368+Y407+F405+E357; wherein said wild-type CH3 domain of the human antibody heavy chain constant region is a CH3 domain of a human IgG1 heavy chain constant region, wherein in said first CH3 domain: said amino acid mutation at T366 is T366W; said amino acid mutation at K409 is K409A; said amino acid mutation at K392 is K392D; said amino acid mutation at Y349 is Y349D; and said amino acid mutation at S354 is S354D; said amino acid mutation at T366 is T366W; said amino acid mutation at K409 is K409A; said amino acid mutation at K392 is K392D; said amino acid mutation at Y349 is Y349D; and said amino acid mutation at S354 is S354D; and wherein in said second CH3 domain: said amino acid mutation at T366 is T366S; said amino acid mutation at L368 is L368A and said amino acid mutation at Y407 is Y407V; or said amino acid mutation at L368 is L368G and said amino acid mutation at Y407 is Y407A; said amino acid mutation at D399 is D399S; said amino acid mutation at F405 is F405K; and said amino acid mutation at E357 is E357A; and wherein said amino acid is numbered according to the EU index of the KABAT numbering of the antibody Fc region. said amino acid mutation at T366 is T366S; said amino acid mutation at L368 is L368A and said amino acid mutation at Y407 is Y407V; or said amino acid mutation at L368 is L368G and said amino acid mutation at Y407 is Y407A; said amino acid mutation at D399 is D399S; said amino acid mutation at F405 is F405K; and said amino acid mutation at E357 is E357A; and wherein said amino acid is numbered according to the EU index of the KABAT numbering of the antibody Fc region.