  The 2d principal models without boundaries have $G\times G$ symmetry. The
already known integrable boundaries have either $H\times H$ or $G_{D}$
symmetries, where $H$ is such a subgroup of $G$ for which $G/H$ is a symmetric
space while $G_{D}$ is the diagonal subgroup of $G\times G$. These boundary
conditions have a common feature: they do not contain free parameters. We have
found new integrable boundary conditions for which the remaining symmetry
groups are either $G\times H$ or $H\times G$ and they contain one free
parameter. The related boundary monodromy matrices are also described.
