Characterizing Riesz Bases via Biorthogonal Riesz-Fischer sequences

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’'.