We present a velocity correction scheme that is suitable for the simulation of the broad range of Mach number flows. The scheme is based on the primitive variable no-iterative algorithm to solving the compressible flow problems, and it uses the high-resolution Kurganov-Tadmor numeric flux scheme. The Kurganov-Tadmor scheme belongs to the class of the central flux schemes produces the correct amount of dissipation to capture the shock waves and other discontinuities in the flow field. The velocity correction scheme is used together with the high-resolution flux to minimize splitting errors and enable low memory footprint during the execution of the code. While the velocity correction scheme makes sure that the splitting errors in pressure-momentum coupling is minimized, special attention is paid to the coupling between the pressure and energy fields, the objective of the newly defined scheme is to provide the tight coupling between velocity, pressure, and temperature fields with the minimum spatial and splitting errors. In addition, the velocity correction scheme provides the natural preconditioning for the flows with the low Mach numbers while maintaining the high resolution of discontinuities at high Mach numbers. The scheme is suitable for applications in incompressible flow applications, and low Mach number variable density flows as well as in transonic and supersonic flow regimes. We include the validation of the newly defined scheme using both inviscid and viscous flows for the wide range of Mach numbers.