Feature selection is an essential preprocessing step for removing redundant or irrelevant features from multidimensional data to improve predictive performance. Currently, medical clinical datasets are increasingly large and multidimensional and not every feature helps in the necessary predictions. So, feature selection techniques are used to determine relevant feature set that can improve the performance of a learning algorithm. This study presents a performance analysis of a new filter and wrapper sequence involving the intersection of filter methods, Mutual Information and Chi-Square followed by one of the wrapper methods: Sequential Forward Selection and Sequential Backward Selection to obtain a more informative feature set for improved prediction of the survivability of breast cancer patients from the clinical breast cancer dataset, SEER. The improvement in performance due to this filter and wrapper sequence in terms of Accuracy, False Positive Rate, False Negative Rate and Area under the Receiver Operating Characteristics curve is tested using the Machine learning algorithms: Logistic Regression, K-Nearest Neighbour, Decision Tree, Random Forest, Support Vector Machine and Multilayer Perceptron. The performance analysis supports the Sequential Backward Selection of the new filter and wrapper sequence over Sequential Forward Selection for the SEER dataset.