We suggest a resource allocation algorithm for multibeam satellite systems over Land Mobile Satellite (LMS) channels. In the satellite system, effectiveness and fairness are conflicting objectives, which can be compromised by scheduling policies, e.g. Proportional fairness scheduling (PFS) and Max-Min fair scheduling. In this paper, we suggest a normalized opportunistic round robin (NOR) algorithm, which is different from opportunistic round robin scheduling (ORR) in the way of allocating beams but the same at the amount of time resource allocated. The NOR algorithm allocates beams based on the normalized channel gains. By normalizing the channel gains, NOR exploits the opportunistic chance from the users channel history, and the differences of average gain among channels are compensated. The unfair resource allocation caused by channel gains is mitigated. As a result, the NOR shows better short term fairness performance than the ORR, especially in the case of highly opposite channel gains. The motivation of this idea is briefly discussed using the probability theory, and supported by simulation results. The next feature of our consideration is fragmentation that is used to transfer large sized data. The DVB-RCS system is based on TCP/IP protocol which divide a packet to several fragment and transmit. We suggest an entire packet transmitting prediction algorithm (PTP) to diminish the total packet loss amount caused by fragment loss due to insufficient channel capacity. This algorithm prevents the system from wasting the channel resource which is used by the packet transmission with insufficient channel capacity. Therefore, users with higher probability of the successful transmission are allocated more bandwidth. The simulation results show that the PTP algorithm provides better performance with fragmentation.