Following the discovery of X-ray absorption in a high velocity outflow from the bright quasar PG1211+143 we have searched for similar features in XMM-Newton archival data of a second ( high accretion rate ) quasar PG0844+349 . Evidence is found for several faint absorption lines in both the EPIC and RGS spectra , whose most likely identification with resonance transitions in H-like Fe , S , and Ne implies an origin in highly ionised matter with an outflow velocity of order \sim 0.2c . The line equivalent widths require a line-of-sight column density of N _ { H } \sim 4 \times 10 ^ { 23 } cm ^ { -2 } , at an ionisation parameter of log \xi \sim 3.7 . Assuming a radial outflow being driven by radiation pressure from the inner accretion disc , as suggested previously for PG1211+143 , the flow in PG0844+349 is also likely to be optically thick , in this case within \sim 25 Schwarzschild radii . If confirmed by better data our analysis suggests that a high velocity , highly ionised outflow is likely to be a significant component in the mass and energy budgets of AGN accreting at or above the Eddington rate .