The growing complexity of systems-on-chip (SoCs) pushes researchers to propose replacing the bus architecture by Networks-on-Chip (NoCs). The key advantages of NoCs are efficient exploitation of performance and scalability. Nowadays NoCs are a well established research topic and several implementations have been proposed. Some techniques are proposed to improve NoC performance in terms of latency and throughput while others are proposed to improve area utilization and power consumption. An important research in NoC design is the tradeoff between area/power and performance. In order to improve performance some techniques tend to increase the number of buffers. However this method increases area and power consumption. This paper introduces new router architecture, called the Flexible Router, which improves the performance of the overall network using the same amount of available buffers but in more efficient way. Therefore there is no need to increase the size of buffers or to use extra virtual channels (VCs) which cause high power consumption, area overheads, and complex logic. The Flexible Router provides a way to handle the requests to a busy buffer by other buffers in the router. It is observed that the Flexible router can achieve better performance in terms of increasing the saturation rate for Hotspot, Uniform, and Nearest-Neighbor traffic patterns, especially Hotspot with an 11.4% increase. Discussion about area overhead compared to the Base router and analysis of arriving out of order packets (side-effect) are also provided.