  The Hill operators $L y = - y^{\prime \prime} + v(x) y, x \in [0,\pi],$ with
$H^{-1}$ periodic potentials, considered with periodic, antiperiodic or
Dirichlet boundary conditions, have discrete spectrum, and therefore, for
sufficiently large $N,$ the Riesz projections $$
  P_n = \frac{1}{2\pi i} \int_{C_n} (z-L)^{-1} dz, \quad C_n=\{z: |z-n^2|= n\}
$$ are well defined. It is proved that $$\sum_{n>N} \|P_n - P_n^0\|^2_{HS} <
\infty, $$ where $P_n^0$ are the Riesz projection of the free operator and
$\|\cdot\|_{HS}$ is the Hilbert--Schmidt norm.
