  For $-1\leq B<A\leq 1$, let $\mathcal{C}(A,B)$ denote the class of normalized
Janowski convex functions defined in the unit disk
$\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$ that satisfy the subordination relation
$1+zf''(z)/f'(z)\prec (1+Az)/(1+Bz)$. In the present article, we determine the
sharp estimate of the Schwarzian norm for functions in the class
$\mathcal{C}(A,B)$. The Dieudonn\'{e}'s lemma which gives the exact region of
variability for derivatives at a point of bounded functions, plays the key role
in this study, and we also use this lemma to construct the extremal functions
for the sharpness by a new method.
