  We use the equations of motion to simplify the general form of
fermion-fermion-Higgs interactions generated by dimension-six gauge-invariant
effective operators. After removing redundant operators it is found that the
most general H f_i f_j vertex for off-shell fermions f_i, f_j and an off-shell
Higgs boson only involves scalar and pseudo-scalar terms, without derivatives.
Examples are presented for the Htt and Htq interactions, where q=u,c, giving
the explicit expressions of the vertices in terms of gauge-invariant operators.
The new operator equalities obtained here also reduce the number of operators
relevant for the Ztq vertices, although the general form of these interactions
is not simplified with respect to previous results.
