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We investigate the effects of higher-order space charge field on the self-deflection of bright screening spatial solitons due to two-photon photorefractive effects by a numerical method under steady-state conditions. The expression for an induced space charge electric field including higher-order space charge field terms is obtained. Numerical results indicate that bright screening solitons undergo self-deflection process during propagation, and the solitons always bend in the opposite direction of the c axis of the crystal. The self-deflection of bright screening solitons can experience considerable increase especially in the regime of high bias field strengths. Relevant examples are provided.