High-entropy alloys have attracted much attention due to their unique microstructures and excellent properties. Since their invention more than ten years ago, research attention has been mainly focused on the study of multicomponent alloys with equiatomic or near-equiatomic compositions. Here we propose a novel design of non-equiatomic medium-entropy alloys that contain one matrix element and several equiatomic alloying elements. To verify the utility of this new design, a series of Co-free Fex(CrNiAl)100-x (at.%, 25 ≤ x ≤ 65) medium-entropy alloys were designed from the much-studied FeNiCrCoAl high-entropy alloy. Detailed characterization reveals that the alloys exhibit novel two-phase microstructures consisting of B2-ordered nanoprecipitates and BCC-disordered matrix. As the alloys deviate far from equiatomic composition, the structure of the nanoprecipitates transfers from a spinodal-like intertwined structure to a nanoparticle dispersed structure. Previous parametric approaches to predict phase formation rules for high-entropy alloys are unable to describe the phase separation behaviors in the studied alloys. Our findings provide a new route to design medium-entropy alloys and also demonstrate a strategy for designing nanostructured alloys from multicomponent alloy systems through simple variations in non-equiatomic compositions.