  The problem of constructing the $SL(N,\mathbb{C})$ invariant solutions to the
Yang-Baxter equation is considered. The solutions ($\mathcal{R}$-operators) for
arbitrarily principal series representations of $SL(N,\mathbb{C})$ are obtained
in an explicit form. We construct the commutative family of the operators
$\mathcal{Q}_k(u)$ which can be identified with the Baxter operators for the
noncompact $SL(N,\mathbb{C})$ spin magnet.
