Complementary to the well-established northern current Mediterranean Outflow around the Iberian margin, we show evidence for the MOW-upper branch veering south along the Moroccan margin, in the Gulf of Cadiz. For that we used new datasets of current velocity (sortable silt) and water mass origin (O and C isotopes of benthic foraminifera). Intense MOW is characteristic of contourite deposits (element ratios from XRF-scan, physical properties) which concurs at millennial variability like Heinrich stadial and Younger Dryas abrupt climate events (O and C isotopes of planktonic foraminifera, foraminifera species, and Sea Surface Temperature-simmax transfer function).