A fluid dispenser including a reservoir forming a neck presenting a thread, a dispenser member, and a fastener system including a fastener ring provided with assembly means for assembling on the thread of the neck in such a manner that the ring is unscrewable from the neck over an axial unscrewing stroke. The outer wall of the neck is provided with a shoulder, and the fastener system includes a security band engaged on the fastener ring. The band axially abuts the shoulder and is secured to the fastener ring at the end of the unscrewing stroke, so as to prevent the fastener system from being removed from the neck immediately after the fastener ring has been unscrewed. The security band includes an unblocking mechanism for disengaging the band from its axial abutment with the shoulder of the neck.