  Anomalously localized states (ALS) at the critical point of the Anderson
transition are studied for the SU(2) model belonging to the two-dimensional
symplectic class. Giving a quantitative definition of ALS to clarify
statistical properties of them, the system-size dependence of a probability to
find ALS at criticality is presented. It is found that the probability
increases with the system size and ALS exist with a finite probability even in
an infinite critical system, though the typical critical states are kept to be
multifractal. This fact implies that ALS should be eliminated from an ensemble
of critical states when studying critical properties from distributions of
critical quantities. As a demonstration of the effect of ALS to critical
properties, we show that the distribution function of the correlation dimension
of critical wavefunctions becomes a delta function in the thermodynamic limit
only if ALS are eliminated.
