  We propose to combine the Trotter decomposition and a series expansion of the
partition function for Hund's exchange coupling in a quantum Monte Carlo (QMC)
algorithm for multiorbital systems that preserves spin and orbital rotational
symmetries. This enables us to treat the Hund's (spin-flip and pair-hopping)
terms, which is difficult in the conventional QMC method. To demonstrate this,
we first apply the algorithm to study ferromagnetism in the two-orbital Hubbard
model within the dynamical mean-field theory (DMFT). The result reveals that
the preservation of the SU(2) symmetry in Hund's exchange is important, where
the Curie temperature is grossly overestimated when the symmetry is degraded,
as is often done, to Ising (Z$_2$). We then calculate the $t_{2g}$ spectral
functions of Sr$_2$RuO$_4$ by a three-band DMFT calculation with tight-binding
parameters taken from the local density approximation with proper rotational
symmetry.
