  We propose a deformed version of the commutation rule introduced in 1967 by
Buchdahl to describe a particular model of the truncated harmonic oscillator.
The rule we consider is defined on a $N$-dimensional Hilbert space $\Hil_N$,
and produces two biorhogonal bases of $\Hil_N$ which are eigenstates of the
Hamiltonians $h=\frac{1}{2}(q^2+p^2)$, and of its adjoint $h^\dagger$. Here $q$
and $p$ are non-Hermitian operators obeying $[q,p]=i(\1-Nk)$, where $k$ is a
suitable orthogonal projection operator. These eigenstates are connected by
ladder operators constructed out of $q$, $p$, $q^\dagger$ and $p^\dagger$. Some
examples are discussed.
