A turbine blade for a turbine engine having a cooling system in the turbine blade formed from at least one leading edge cooling chamber for cooling the leading edge and for exhausting cooling fluids through a tip exhaust outlet. The leading edge cooling channel may include a second section that extends radially inward from the tip exhaust outlet and a first section that extends radially inward from the second section along the leading edge. The second section may be narrower than the first section and may direct cooling fluids to be exhausted from tip exhaust outlet skewed angle towards the suction side of the blade. As such, the leading edge cooling channel and tip exhaust outlet cooperate to exhaust the cooling fluids without forming a separation zone at the upstream side of the intersection between the leading edge cooling channel and the tip exhaust outlet.