  In this note we prove that if two Riesz-Fischer sequences in a separable
Hilbert space $H$ are biorthogonal and one of them is complete in $H$, then
both sequences are Riesz bases for $H$. This complements a recent result by D.
T. Stoeva where the same conclusion holds if one replaces the phrase
``Riesz-Fischer sequences'' by ``Bessel sequences''.
