  Statistical properties of non--symmetric real random matrices of size $M$,
obtained as truncations of random orthogonal $N\times N$ matrices are
investigated. We derive an exact formula for the density of eigenvalues which
consists of two components: finite fraction of eigenvalues are real, while the
remaining part of the spectrum is located inside the unit disk symmetrically
with respect to the real axis. In the case of strong non--orthogonality,
$M/N=$const, the behavior typical to real Ginibre ensemble is found. In the
case $M=N-L$ with fixed $L$, a universal distribution of resonance widths is
recovered.
