We consider the Jack–Laurent symmetric functions for special values of parameters p
0=n+k
−1
m, where k is not rational and m and n are natural numbers. In general, the coefficients of such functions may have poles at these values of p
0. The action of the corresponding algebra of quantum Calogero–Moser integrals
$\mathcal{D}$
(k, p
0) on the space of Laurent symmetric functions defines the decomposition into generalised eigenspaces. We construct a basis in each generalised eigenspace as certain linear combinations of the Jack–Laurent symmetric functions, which are regular at p
0=n+k
−1
m, and describe the action of
$\mathcal{D}$
(k, p
0) in these eigenspaces.