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There is presently a high interest in the spatial industry to develop high-performance on-board processing platforms with a high degree of flexibility, so they can adapt to varying mission needs and/or to future space standards. For this purpose, Field Programmable Gate Array (FPGA) devices have demonstrated to offer an excellent compromise between flexibility and performance. This work presents a novel FPGA-based architecture to be used as part of the hyperspectral linear unmixing processing chain. In particular, this paper introduces a new architecture for hyperspectral endmember extraction accordingly to the Modified Vertex Component Analysis (MVCA) algorithm, which provides a better figure of merit in terms of endmember extraction accuracy versus computational complexity than the Vertex Component Analysis (VCA) algorithm. Two versions of the MVCA algorithm which differ on the use of floating point or integer arithmetic for iteratively projecting the hyperspectral cube onto a direction orthogonal to the subspace spanned by the endmembers already computed have been mapped onto a Xilinx Virtex-5 FPGA. The results demonstrate that both versions are capable of processing hyperspectral images captured by the NASA's AVIRIS sensor in real-time, showing the latter a better performance in terms of hardware resources and processing speed. Furthermore, our proposal constitutes the first published architecture for extracting the endmembers from a hyperspectral image based on the VCA principle and thus, it provides a basis for future FPGA implementations of state-of-the-art hyperspectral algorithms with similar characteristics, such as the Automatic Target Generation Process (ATGP) or the Orthogonal Subspace Projection (OSP) algorithms.