We experimentally show that, in contrast to the data having been collected so far, some single crystals of NaNbO(3) exhibit a dielectric permittivity of several thousand, at low T, and this value is saturated when approaching 0 K on cooling. Other sodium niobate crystals (having larger dielectric losses) present a first-order phase transition to a ferroelectric phase on cooling (at 80-200 K). The width of the thermal hysteresis in these crystals increases when the temperature of the phase transition obtained on heating decreases. The dielectric permittivity at the phase transition obtained on cooling shows a tendency to increase and saturate, when the thermal hysteresis increases. We identify the ground state of the sodium niobate crystal exhibiting the smallest dielectric losses (in the studied set of crystals) as a novel quantum paraelectric state coexisting with a metastable ferroelectric state. In principle, the crystal presenting the state of quantum paraelectricity can be considered as having the largest (among the crystals studied) thermal hysteresis, for which the low boundary is below 0 K.