  We describe non-conventional localization of the midband E=0 state in square
and cubic finite bipartite lattices with off-diagonal disorder by solving
numerically the linear equations for the corresponding amplitudes. This state
is shown to display multifractal fluctuations, having many sparse peaks, and by
scaling the participation ratio we obtain its disorder-dependent fractal
dimension $D_{2}$. A logarithmic average correlation function grows as $g(r)
\sim \eta \ln r$ at distance $r$ from the maximum amplitude and is consistent
with a typical overall power-law decay $|\psi(r)| \sim r^{-\eta}$ where $\eta $
is proportional to the strength of off-diagonal disorder.
