The sheer volume of biomedical text is growing at an exponential rate. This growth creates challenges for both human readers and automatic text processing algorithms. One such challenge arises from common and uncontrolled usages of abbreviations in the biomedical literature. This, in turn, requires that biomedical lexical ontologies be continuously updated. In this paper, we propose a hybrid approach combining lexical analysis techniques and the Support Vector Machine (SVM) to create an automatically generated and maintained lexicon of abbreviations. The proposed technique is differentiated from others in the following aspects: 1) It incorporates lexical analysis techniques to supervised learning for extracting abbreviations. 2) It makes use of text chunking techniques to identify long forms of abbreviations. 3) It significantly improves Recall compared to other techniques. The experimental results show that our approach outperforms the leading abbreviation algorithms, ExtractAbbrev and ALICE, at least by 6% and 13.9%, respectively, in both Precision and Recall on the Gold Standard Development corpus.