A new generalization of the flux-corrected transport (FCT)
methodology to implicit finite element discretizations is
proposed. The underlying high-order scheme is supposed to be
unconditionally stable and produce time-accurate solutions
to evolutionary convection problems. Its nonoscillatory
low-order counterpart is constructed by means of mass
lumping followed by elimination of negative off-diagonal
entries from the discrete transport operator. The raw
antidiffusive fluxes, which represent the difference between
the high- and low-order schemes, are updated and limited
within an outer defect correction loop. The upper bound for
the magnitude of each antidiffusive flux is evaluated using
a single sweep of the multidimensional FCT  limiter at the
first outer iteration. This semi-implicit limiting strategy
makes it possible to enforce the positivity constraint
in a very robust and efficient manner. Moreover, the
computation of an intermediate low-order solution
can be avoided. Numerical examples are presented
for two-dimensional benchmark problems discretized
by the standard Galerkin FEM combined with the
Crank-Nicolson time-stepping.