The present invention pertains to turbine engine mounting onto an aircraft pylon, comprising a bracket (12) arranged to be attached to the pylon, a lever (15;15′) attached in its central part (150;150′) to the bracket by first connection means (150-130) with a pivot pin (136;136′) and two thrust links (20,22; 20′,22′) each joined aft to the lever by second connection means (200-155, 220-157; 200′-155′; 220′-157′) and including engine attachment means at the forward end, characterized in that the first connection means (150-130) consists of two parallel arms (151,153) spaced apart on central part (150) of the lever, cooperating with an attachment lug (130) integral with the bracket via a pivot pin, and lever (15,15′) comprises two third side connection means on standby (155-135, 157-137; 155′-135′; 157′-137′) with bracket (12,12′). The invention provides for simplified mounting with improved safety.