A fluid dispenser comprising: a fluid reservoir (1) having a neck (11) defining an opening (10) and an axis X, the neck (11) projecting axially from a shoulder (13); and a dispenser unit (D) comprising a dispenser member (4), such as a pump or a valve, and a fastener system (2, 31) for fastening the dispenser member (4) on the neck (11) of the reservoir (1), the fastener system comprising a fastener ring (2) that is engaged with the neck (11) and a blocking hoop (31) that is engaged axially around the ring (2) for blocking the ring on the neck in the final assembled position; disassembly means (14, 34) for axially moving the hoop (31) relative to the ring (2), from the final assembled position to a disassembled position in which the hoop does not block the ring on the neck, such that the unit (D) can be removed from the neck (11), the disassembly means comprising two elements (14, 34) capable of turning mutually relative to each other about the axis X, the dispenser being characterized in that one element (14) of the disassembly means is secured to the reservoir, while an other element (34) is secured to the dispenser unit (D).