This paper proposes a new test compression technique that employs Fan-out SCAN chain with Feedback (FSCANF) architecture. It allows us to use prelude vectors to resolve dependencies created by fanning out multiple scan chains from a single scan-in pin. This paper describes the new proposed architecture as well as the algorithm that generates compressed test vectors using vertex coloring algorithm. The distribution of specified bits in each test pattern determines the compression ratio of the individual test pattern. Therefore, our technique optimizes the overall compression ratio and shows higher reduction in test data and application time than previous techniques, which use the extreme case of serializing all the scan chains in the presence of conflicts across the fan-out scan chains.The FSCANF architecture has small hardware overhead and is independent of scan cell orders in the scan chains. Experimental results show that our technique significantly reduces both the test data volume and test application time in six of the largest ISCAS 89 sequential benchmark circuits compared to the previous techniques.