Linear Graph Embedding (LGE) is the linearization of graph embedding, which could explain many of the popular dimensionality reduction algorithms such as LDA, LLE and LPP. LGE algorithms have been applied in many domains successfully; however, those algorithms need a PCA transform in advance to avoid a possible singular problem. Further, LGEs are non-orthogonal and this makes them difficult to reconstruct the data. Some orthogonal LGEs have more discriminating power than their counterparts of LGEs, but the experiments imply that their robustness should be improved. Moreover, those orthogonal LGEs also need a PCA transform. Using PCA as preprocessing can reduce noise and avoid the singular problem, but some discriminative information also is abandoned. In this paper, we present an Orthogonal LGE algorithm (Orthogonal Direct LGE) to extract features from the original data set directly by solving common Eigen value problem of symmetric positive semi definite matrix. Orthogonal LGE shares the excellence of LGEs and OLGEs. Moreover, Orthogonal LGE is least-squares normalized Orthogonal, while OLGEs is not known to be optimal for LGEs in any sense. Experimental results demonstrate the effectiveness and robustness of our proposed algorithm.