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We present some new results about covariants in small characteristic. Insection 1, we give a method to construct covariants using an approach similarto Sturmfels. We apply our method to find a separating system of covariants forbinary quartic in characteristic 3. In the second section, we construct a newoperator on covariants when the characteristic is small compared to the degreeof the form.

A strategy and a new operator to generate covariants in small characteristic