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It is well known that, in any inner product space, a set of linearlyindependent (LI) vectors can be transformed to a set of orthogonal vectors,spanning the same space, by the Gram-Schmidt Orthogonalization Method (GSOM).In this paper, we propose a transformation from a set of LI vectors to a set ofLI non orthogonal yet energy (square of the norm) preserving (LINOEP) vectorsin an inner product space and we refer it as LINOEP method. We also show thatthere are various solutions to preserve the square of the norm.

The Linearly Independent Non Orthogonal yet Energy Preserving (LINOEP) vectors