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In this paper, a new technique called two- directional two-dimensional Fisher principal component analysis ((2D)2FPCA) in the two dimensional principal component analysis (2DPCA) transformed space is analyzed and its nature is revealed. We first argue that the standard 2D-PCA method works in the column direction of images and subsequently we propose an alternate 2D-FLD which works in the row direction of images in the 2DPCA subspace. To straighten out the problem of massive memory requirements of the 2D-PCA method and as well the alternate 2D-FPCA method, we introduce (2D)2FPCA method. The introduced (2D)2FPCA method has the advantage of higher recognition rate, lesser memory requirements and better computing performance than the standard PCA /2D-PCA /2D-FLD/2D-FPCA method, and the same has been revealed through extensive experimentations conducted on Finger-Vein dataset.