  We consider the Haar functions $h_I$ on dyadic intervals. We show that if
$p>\frac23$ and $E\subset[0,1]$ then the set of all functions
$\|h_I1_E\|_2^{-1}h_I1_E$ with $|I\cap E|\geq p|I|$ is a Riesz sequence. For
$p\leq\frac23$ we provide a counterexample.
