Characteristics of quasi-single-helicity (QSH) states have been studied in a low-aspect-ratio reversed field pinch (RFP) machine RELAX mainly by magnetic diagnostics. Internal profiles of the fluctuating radial, poloidal and toroidal magnetic fields have shown good agreement with eigenfunctions of a single helical mode. The edge magnetic fluctuation spectra are somewhat broader than what are expected from internal magnetic field profiles. In spite of these slight discrepancies, the usual measure for the QSH, the spectral index N S lower than 2, still provides a reasonable measure for QSH states in RELAX. The QSH persistence has been improved in RELAX by the reduction of the poloidal resistance of flanges at poloidal gaps, mainly due to the improved axisymmetry of the toroidal magnetic field. QSH persistence more than 30% of the flat-topped current phase has been realized with current density lower than in other RFP, and probability of spontaneous QSH is 12.8 ± 7.3% which is higher than high-aspect-ratio RFP. It suggests the advantage of low-aspect-ratio configuration in attaining to the QSH. Comparison with recent experiments using active resonant perturbation may suggest the importance of further reduction of field errors to improve the quality of QSH.