The bright X-ray binary X2127 + 119 in the core of the globular cluster M15 has long been thought to be in an unusual evolutionary state, in which the binary is embedded in a common envelope. Support for this idea comes from the absorption lines of X2127 + 119, which are blueshifted at all orbital phases, indicating the existence of outflows from the system. A common-envelope scenario implies that the absorption lines should exhibit maximum blueshift near mid-eclipse (binary phase 0.0). We have re-analysed Isaac Newton Telescope spectra of X2127 + 119 obtained in 1986, 1987 and 1988 using the latest orbital ephemeris (substantially different from that used in the original analysis), and find that the orbital phase at which the absorption lines show a maximum blueshift is not 0.0, but rather 0.25-0.3. These results indicate that a common-envelope scenario for X2127 + 119 may not work. In addition, from spectrograms of the He II λ4686 line, we report the first tentative detection of the companion star of X2127 + 119.