A Pythagorean $(k,l)$-tuple over a commutative ring $A$ is a vector $(x_1,\cdots ,x_{k+l})\in A^{k+l}$ such that $x_1^2+\cdots +x_k^2=x_{k+1}^2+\cdots +x_{k+l}^2$. In the present paper, the authors give a polynomial parametrization of Pythagorean $(k,l)$-tuples over the ring $F\left[t\right]$ (where $F$ is a field), for $l\ge 2$. They also give the solutions for the cases $l=1$ and $k=2,3,4,5,9$.