Classification of nonlinearly separable data by nonlinear support vector machines is often a difficult task, especially due to the necessity of a choosing a convenient kernel type. Moreover, in order to get high classification accuracy with the nonlinear SVM, kernel parameters should be determined by using a cross validation algorithm before classification. However, this process is time consuming. In this study, we propose a new classification method that we name Support Vector Selection and Adaptation (SVSA). SVSA does not require any kernel selection and it is applicable to both linearly and nonlinearly separable data. The results show that the SVSA has promising performance that is competitive with the traditional linear and nonlinear SVM methods.