  In this paper, we construct framelets associated with a sequence of
quadrature rules on the simplex $T^{2}$ in $\mathbb{R}^{2}$. We give the
framelet transforms -- decomposition and reconstruction of the coefficients for
framelets of a function on $T^{2}$. We prove that the reconstruction is exact
when the framelets are tight. We give an example of construction of framelets
and show that the framelet transforms can be computed as fast as FFT.
