We report the discovery of a new detached, double white dwarf (WD) system with an orbital period of 39.8 min. We targeted SDSS J163030.58+423305.8 (hereafter J1630) as part of our radial velocity programme to search for companions around low-mass WDs using the 6.5-m MMT. We detect peak-to-peak radial velocity variations of 576 km s-1. The mass function and optical photometry rule out main-sequence companions. In addition, no millisecond pulsar companions are detected in radio observations. Thus the invisible companion is most likely another WD. Unlike the other 39-min binary SDSS J010657.39-100003.3, follow-up high-speed photometric observations of J1630 obtained at the McDonald 2.1-m telescope do not show significant ellipsoidal variations, indicating a higher primary mass and smaller radius. The absence of eclipses constrain the inclination angle to i≤ 82°. J1630 contains a pair of WDs, 0.3 M&sun; primary +≥0.3 M&sun; invisible secondary, at a separation of ≥0.32 R&sun;. The two WDs will merge in less than 31 Myr. Depending on the core composition of the companion, the merger will form either a single core He-burning subdwarf star or a rapidly rotating massive WD. The gravitational wave strain from J1630 is detectable by instruments like the Laser Interferometer Space Antenna (LISA) within the first year of operation. Based on observations obtained at the MMT Observatory, a joint facility of the Smithsonian Institution and the University of Arizona.