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Grid computing is the ultimate framework that provides a high performance computing environment to meet growing and larger scale computational demands. However, Grid Computing is a critical and complex undertaking as the management of resources and computational jobs are geographically distributed under the ownership of different individuals or organizations with their own access policies, dynamic availability and heterogeneous in nature. Therefore, it is a big challenge and pivotal issue to design an efficient job scheduling algorithm for implementation in the real grid system. Various works has been done by many researchers, still further analysis and research needs to be done to design new techniques and improve the performance of scheduling algorithm in grid computing. The main purpose of this paper is to develop an efficient job scheduling algorithm to maximize the resource utilization and minimize processing time of the jobs. The proposed job scheduling is based on job grouping concept taking into account memory constraint together with other constraints such as processing power, Bandwidth, expected execution and transfer time requirements of each job. These very constraints are taken at job level rather than at group level. The experimental results demonstrate that the proposed scheduling algorithm efficiently reduces the processing time of jobs in comparison to others.