Global System for Mobile (GSM) is a second generation cellular standard developed to cater voice services and data delivery using digital modulation. Short Message Service (SMS) is the text communication service component of mobile communication systems, using standardized communications protocols that allow the exchange of short text messages between mobile phone devices. SMS will play a very vital role in the future business areas whose are popularly known as m- Commerce, mobile banking etc. For this future commerce, SMS could make a mobile device in a business tool as it has the availability and the effectiveness. The existing SMS is not free from the eavesdropping, but security is the main concern for any business company such as banks who will provide these mobile banking. Presently there is no such scheme which can give the complete SMS security. Now, a new security scheme for improving the SMS security is proposed here. At first plaintext of SMS would be made as cipher text with the help of existing GSM encryption technology, then this cipher text would be digitally signed with the help of public key signature. These will be made compatible to existing infrastructure of GSM security. The proposed scheme will give total authenticity, data integrity, confidentiality, authorization and non-repudiation which are the most essential issues in m-commerce or mobile banking and in secure messaging.