After observing the launch of a new space platform, Z.O.W.I.E. (Zonal Organisation World Intelligence Espionage) Chief Lloyd C. Cramden joins President Trent (Andrew Duggan) for a game of golf. While on the links they are interrupted by a small group, two women disguised as boys and an actor disguised as an old man, all from the Fabulous Face organization. Discreetly substituting the presidential golf ball with a small gas bomb they succeed in temporarily immobilizing the presidential party and replacing the president with the now-undisguised actor, who has been surgically altered to look exactly like him. The Fabulous Face organization has conceived a plot to gain control of the world and run it entirely by a group of women led by Elisabeth (Anna Lee); Cramden has more-or-less inadvertently stumbled upon this world-domination plot. The women want to establish a matriarchy, and the first step in their plan is to gain control of a US space facility in the Virgin Islands. Elisabeth has established the spa there as a cover. The women establish their headquarters near the rocket base to brainwash their male-oriented sisters by planting tape recorders in their hair dryers.