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The formulae of the relationships between Euler angles and texture are important for the orientation distribution functions of research materials. At present, it is found that the formulae for the orthogonal and hexagonal crystal structure proposed by Roe and Bunge are not in accord with the normal direction ( ND) being perpendicular to the rolling direction ( RD) . In this paper, these formulae are deduced independently according to the notations proposed by Roe and Bunge. The results show that in addition to the coincidence with the formulae for the cubic crystal structure given by the Roe and Bunge, the other formulae are different from Roe \' s and Bunge \' s. The new formulae are in accord with ND, RD, and transverse direction ( TD) at right angles.