There is a need for an intense, unmodulated single-frequency stabilized laser light that guarantees absolute optical frequency in a rapid laser calibration or an ultra-high resolution interferometer. To obtain such a light, we developed a new laser system that uses an intermittent frequency offset lock of a symmetric three-mode stabilized He-Ne laser to an iodine stabilized He-Ne laser. The proposed laser system provides two operational modes: (1) independent and (2) slave mode. In the independent mode, frequency of the three-mode laser is stabilized via control of frequency difference between two intermode beats. The resultant output is a single longitudinal mode light of maximum intensity that locates at the top of the gain curve. Frequency instability of 8X10^-12 (at a sampling time of 100 s) which is better than conventional stabilized lasers is attained in the independent mode. Slow optical frequency drift during the independent mode is periodically corrected by the offset lock to the iodine stabilized laser (slave mode), resulting in accurate reset of the frequency drift. After reset of the frequency deviation, the three-mode laser is again operated in the independent mode. Due to such intermittent offset lock, duty factor of the iodine stabilized laser was reduced to a few % of continuous operation.