Abstract: The motion of a charged relativistic particle in the （E2 〉H2） uniform orthogonal electromagnetic field is studied by solving the equation of motion in a special frame in which the field becomes purely electric, and then transforming the solution under a Lorentz boost. The three-dimensional vector expression of the particle＇ s relativistic motion is obtained and the corresponding trajectories in Cartesian coordinate are graphed by using software Mathematlea

Key words: orthogonal electromagnetic field, charged particle, relativistic motion