In the latest step for CIM Group’s still mysterious Drake Hotel site project, luxury jeweler Buccellati is giving up its retail townhouse lease at 46 E. 57th St. and moving to 810 Madison Ave.

Prudential Douglas Elliman’s Faith Hope Consolo and Joseph Aquino orchestrated the complex, two-pronged deal. Buccellati has already closed its 57th Street store after four decades there and will soon open a two-level boutique at 810 Madison between 67th-68th Streets.

It wasn’t known how much Buccellati is paying for its new, 2,000 square-foot home. The asking rent was $1,000 a square foot. Cushman & Wakefield repped the landlord at 810 Madison.

CIM now owns and controls all the townhouses from 42-50 E. 57th St. except for no. 48, still owned by Jacob & Co., which thus far has declined to sell.