Scheelite (CaWO4) is one of the main raw material for the production of tungsten. It is usually encountered in skarn deposits where it is commonly associated with other calcium minerals as fluorite, apatite, and calcium silicates. Worldwide, scheelite is upgraded to the chemical grades by direct flotation, but the separation efficiency remains limited due to similar flotation behaviors of scheelite and gangue minerals with fatty acid. The only solutions used to overcome this issue involve high energy consumption or ecotoxic reagents. In the present study, a novel method based on the use of a centrifugal Falcon concentrator was investigated to perform an efficient elimination of gangue minerals and fine particles as well as an acceptable scheelite recovery enabling a decrease of the flotation reagents consumption. The performances of the two types of laboratory Falcon bowls, Falcon UltraFine (UF) and Falcon Semi-Batch (SB), were modeled using the design of experiments (DoE) methodology, which allowed to determine the best operating parameters for each bowl. The separation performances were mainly affected by the rotary speed and the pulp density for the Falcon UF and by the rotary speed and the fluidization pressure for the Falcon SB. Due to the fluidization pressure, the Falcon SB exhibited higher gangue minerals rejection with slightly lower recoveries than the Falcon UF. Overall, the optimized Falcon SB test allowed to reach 71.6%, 22.6%, 17.2%, and 12.6% for scheelite, calcium salts, dense calcium silicates, and light non-calcic silicates respectively while the desliming efficiency reached 98.8%. For comparison purposes, a classical hydrocyclone allowed to attain 89.1%, 89.3%, 79.5%, and 76.5% for scheelite, calcium salts, dense calcium silicates, and light non-calcic silicates respectively while the desliming efficiency reached 52.0%. Theses results can be used reliably to assess the separation performances of an industrial Falcon C which can be regarded, along with Falcon SB, as a sustainable and efficient gangue rejection method for complex W skarn ore, which allows the use of environmentally friendly reagents during downstream flotation stages.