  All cubic couplings in type IIB supergravity on $AdS_5\times S^5$ that
involve two scalar fields $s^I$ that are mixtures of the five form field
strength on $S^5$ and the trace of the graviton on $S^5$ are derived by using
the covariant equations of motion and the quadratic action for type IIB
supergravity on $AdS_5\times S^5$. All corresponding three-point functions in
SYM$_4$ are calculated in the supergravity approximation. It is pointed out
that the scalars $s^I$ correspond not to the chiral primary operators in the
${\cal N}=4$ SYM but rather to a proper extension of the operators.
