We report on the conception, fabrication and characterization of a new concept of optical fiber enabling a precise control of the ratio between the 2nd and 4th-order of chromatic dispersion (respectively β2 and β4) at 1.55 µm which is at the heart of the Four-Wave-Mixing (FWM) generation. For conventional highly nonlinear fiber the sensitivity of this ratio to fiber geometry fluctuations is very critical, making the fabrication process challenging. The new design fiber reconciles the accurate control of chromatic dispersion properties and fabrication by standard stack and draw method, allowing a robust and reliable method against detrimental fluctuations parameters during the fabrication process. Experimental frequency conversion with FWM in the new design fiber is demonstrated.