After explaining the paradox of the cage-like freedom, a result of being liberated through the death of God and the nature of all life as a will to power, Friedrich Nietzsche predicts the next step in human evolution, the ubermensch (or overman). Nietzsche's outline for the overman as a possible to solution to the paradox of freedom is prevalent in the film Fight Club.
The overman, says Nietzsche, must be willed: we must not be content with our current state of mediocrity, but strive for perfection. Nietzsche points out, though, that if perfection is accomplished, then the process has ended, and growth ceases. The overman seeks to overcome everything she/he has internalized from external sources, especially society and religion. "The striving for distinction," as Nietzsche calls it, is the process of creating something that is truly one's own (a self); through the will to power, the overman reaches self-realization, but does not stop there. Because of the "will of spirit," the overman continually creates a new self by surpassing (overcoming) the old self: by continually taking risks and always accepting responsibility for her/his actions and vaules, the overman lives by her/his self-created values, realizing she/he is these actions, thus acquiring freedom through growth.
Fight Club's protagonist, "Jack" proclaims that he was "close to being complete," to which his alter-ego, Tyler, responds "Never be complete, stop being perfect; I say let's evolve." Tyler echoes Nietzsche's advocation that man should will the overman, and gives Jack the insight that "The things you own end up owning you." When the film begins, Jack has not yet realized that his life has become defined by external sources and not his own will, but he is introduced to Tyler's philosophy that "Self destruction could be the answer".
Later in the film, Jack tells a police investigator "That wasn't just stuff that got destroyed, that was me": he believes that his possessions create his identity (self), but he beings listening to Tyler, who spouts such insight as "It's only after we've lost everything that we're free to do anything." Here Tyler refers to the overman's process of overcoming those aspects of one's self not truly one's creation, but an internalization of external sources.
The theme of the overman as self-creating is exemplified in the film: Tyler tells Jack "You are not your job...the contents of your wallet...your sic. khakis," and once Jack realizes that he is Tyler, he sees that he has created his self. Only when Jack takes responsibility for his creation of Tyler does he experience growth (as per Nietzschean guidelines) and understand his freedom from putting society in the place of God as he had formerly done. Nietzsche would explain Jack's creation of a new person by the end of the film as the will of his spirit and his having overcome everything within him, including his self-created self Tyler. Thus Jack, as the overman in Fight Club, takes responsibility for his actions and values, and endures the process of self-overcoming: he calls the end of the film "the beginning," stating, "My eyes are open. Everything's gonna be fine."