  In this paper, we introduce a class of $B$-splines on the Heisenberg group
$\mathbb{H}$ and study their fundamental properties. Unlike the classical case,
we prove that there does not exist any sequence $\{\alpha_n\}_{n\in\mathbb{N}}$
such that
$L_{(-n.-\frac{n}{2},-\alpha_n)}\phi_n(x,y,t)=L_{(-n.-\frac{n}{2},-\alpha_n)}\phi_n(-x,-y,-t)$,
for $n\geq 2$, where $L_{(x,y,t)}$ denotes the left translation on
$\mathbb{H}$. We further investigate the problem of finding an equivalent
condition for the system of left translates to form a frame sequence or a Riesz
sequence in terms of twisted translates. We also find a sufficient condition
for obtaining an oblique dual of the system
$\{L_{(2k,l,m)}g:k,l,m\in\mathbb{Z}\}$ for a certain class of functions $g\in
L^2(\mathbb{H})$. These concepts are illustrated by some examples. Finally, we
make some remarks about $B$-splines regarding these results.
