Suppose that \(H^\infty\) is the set of bounded analytic functions in the unit disk \(D\) and that \(T=\partial D\). A Blaschke product \(B(z)\) is a bounded analytic function of the form \[ B(z)= z^m \prod_{n=1}^\infty \frac{-\overline{z}_n} {|z_n|} \frac{z- z_n} {1-\overline{z}_n} \quad \text{where } \sum(1-|z_n|)< \infty,\;|B(e^{i\theta})|=1 \text{ a.e.} \] A sequence \(\{z_n\}\subset D\) is called interpolating if every interpolation problem \(f(z_n)= w_n\), \(\{w_n\}\in l^\infty\) has a solution in \(H^\infty\). A Blaschke product whose zero set is an interpolating sequence is called an interpolating Blaschke product. The author gives a new proof of the theorem of Jones which says that every unimodular function in \(L^\infty(T)\) can be uniformly approximated by the ratio of two interpolating Blaschke products. The proof uses ideas of Garnett and Nicolau which were used to prove that every function in \(H^\infty\) can be uniformly approximated by a linear combination of interpolating Blaschke products. In particular, let \(K\) be the closed convex hull of the interpolating Blaschke products. Garnett and Nicolau proved that for any \(h\in H^\infty\), there exists a constant \(c_f\) such that \(f\in c_f K\). It is unknown whether every \(H^\infty\) function of unit norm is contained in \(K\). The author proves that every \(H^\infty\) function of sufficiently small norm is contained in \(K\). He remarks that \(|f|< 10^{-1000}\) is sufficiently small.