This paper discusses the orthogonalisation in Gram-Schmidt algorithms. Four variants of Gram-Schmidt procces are presented and the relation between matrix size and running time for computation is also discussed. Loss of orthogonality of the computed vectors in Gram-Schmidt process can be reduced to be close to the machine precision level by reorthogonalisation. Theoretically the loss of orthogonality is bounded and it is true that reorthogonalisation in Gram-Schmidt procces work well when the computation is not overflow. however when reorthogonalisation is applied the backward error is becoming larger.