The resilient S-boxes have applications in fault tolerant distributed computing, quantum cryptographic key distribution and random sequence generation for stream ciphers. Based on the use of linear error correcting codes together with highly nonlinear S-Boxes, a new construction of highly nonlinear resilient S-boxes with given degree is provided. A contribution of the construction is that the nonlinearity of the resilient S-boxes can be calculated with the parameter of the linear code. As a result, the construction provides currently the best results in the aspect of nonlinearity.