A new phase transition is observed in the KLiSO4 crystals below 77 K using MoO43- as a paramagnetic probe. The EPR spectra of this molecular ion, which substitutes for the host SO42- ion, show triclinic symmetry at 77 K due to the joint action of a trigonal crystal field and a trigonal Jahn-Teller effect of E(X)e type. Above 77 K, motional averaging in the a-b plane occurs; thereby an axial spectrum is observed. Below 64 K, the two sulphate sites are no longer equivalent resulting in the appearance of two distinct EPR spectra of the molybdate ion. The possible space groups of the crystal in the vicinity of the phase transition are discussed. The authors' results indicate that one needs to distinguish carefully between the local dynamics and the structural changes in this crystal.