A novel technique, named "core suction," for fabricating optical fiber preforms has been devised. The technique involves drawing the molten nonconventional core glass material into the cladding tube to form the preform. The developed technique is simple, inexpensive, and shows great potential for fabricating preforms of highly nonlinear nonconventional glasses as the core material. Preforms were made with Schott SF6 and a lead-tellurium-germanate glass in silica cladding tubes, and these preforms were then pulled into fibers.