High-enthalpy arc-heated supersonic wind tunnels are characterized by test gases that are heated by a high-current electric arc and then expanded and accelerated through a convergent-divergent nozzle. In this work, a Mach 4 supersonic nozzle was designed for the Technion Arc-Plasma wind Tunnel (TAPT) according to two different working point conditions characterized by different plenum enthalpies and pressures. The objective was to obtain ideally expanded gas with no shock wave formation at the nozzle exit and accompanying low nozzle temperatures. The initial design was performed using a simplified approach, enabling the examination of feasible design parameters, which were subsequently validated using CFD and finite element structural simulations. The simplified design approach was subdivided into an aerodynamic component (method of characteristics); semi-empirical aerodynamic-heating predictions; empirical nozzle cooling-jacket performance predictions; and structural considerations (based on the pressure and thermally induced stresses). The simplified result showed excellent agreement with CFD predictions and finite element structural simulations. On this basis, a nozzle design procedure was proposed while taking relatively high safety factors into account. The methodology developed in this work is intended to support the facility for all future nozzle designs.