We introduce the operator-valued relative
free entropy $\chi_\mb^{\ast}(X_1,X_2,\cdots,X_n:\mb)$ of a
family of self-adjoint random variables
$X_1,X_2,\cdots,X_n$
in a $\mb$-valued noncommutative probability
space $(\ma,\emb,\mb)$. This notion extends D. Voiculescu's relative
free entropy $\Phi^{\ast}$ which defined in a tracial
W*-noncommutative probability space to a more general context.
The free entropy of a semicircular variable with conditional
expectation covariance can be computed by using the modular frames
and then
we point out the relation between the free entropy of a semicircular variable and the
index of a conditional expectation. At last, we obtain an estimate
of the free entropy dimension $\delta^\ast_{\mb,\tau}$.