Methyltransferase that catalyzes the reduction, ring contraction and methylation of C-17 in cobalt-factor III to form cobalt-precorrin-4. Is also able to convert cobalt-precorrin-3 to cobalt-precorrin-4. AH2 + Co(II)-factor III + S-adenosyl-L-methionine = A + Co-precorrin-4 + S-adenosyl-L-homocysteine Binds 1 [4Fe-4S] cluster. Cofactor biosynthesis; adenosylcobalamin biosynthesis. In the N-terminal section; belongs to the precorrin methyltransferase family.