  In this paper, we will consider a noncommutative probability space, $(T,E),$
over a Toeplitz matricial algebra $B=\QTR{cal}{C}^{N},$ for $N\in
\QTR{Bbb}{N}$, induced by a (scalar-valued) noncommutative probability space,
$(A,\QTR{cal}{\phi}),$ with a suitable $B$-functional, $E:T\to B,$ defined by
$\phi .$ On this framework, we will observe amalgamated R-transform calculus
with respect to a $B$-functional, $E.$ The technique and idea are came from
those in [12] and Free Probability of type $B$ studied in [31].
