The invention relates to the field of rocket engines, and more particularly to a propulsion assembly (10) comprising a first tank (11) for a first liquid propellant, a second tank (12) for a second liquid propellant, a pressurizer device (60) configured to maintain a substantially higher pressure in the second tank (12) than in the first tank (11), and a single-shaft turbopump (30) comprising a turbine (33), a first pump (31), and a second pump (32). The turbine (33) is actuated by expansion of the first propellant after it has passed through a regenerative heat exchanger (44), and in turn it acts via the single rotary shaft (34) of the turbopump (30) to drive said first and second pumps (31, 32) respectively pumping said first and second propellants in order to feed a propulsion chamber (40).