  We investigate strong-coupling properties of a two-dimensional ultracold
Fermi gas in the normal phase. In the three-dimensional case, it has been shown
that the so-called pseudogap phenomena can be well described by a
(non-self-consistent) $T$-matrix approximation (TMA). In the two-dimensional
case, while this strong coupling theory can explain the pseudogap phenomenon in
the strong-coupling regime, it unphysically gives large pseudogap size in the
crossover region, as well as in the weak-coupling regime. We show that this
difficulty can be overcome when one improve TMA to include higher order pairing
fluctuations within the framework of a self-consistent $T$-matrix approximation
(SCTMA). The essence of this improvement is also explained. Since the
observation of the BKT transition has recently been reported in a
two-dimensional $^6$Li Fermi gas, our results would be useful for the study of
strong-coupling physics associated with this quasi-long-range order.
