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Munro, chief of a team of British scientists working on a project to enable man to move through space and time by mental powers, is found dead with his brain exploded. Major Clarke, in charge of security, investigates the death and finds that Americans and Russians working on a similar project have met the same kind of death. Dr. Mark Davidson is appointed to replace Munro, but when Clarke learns that Davidson's wife, Julie, cannot blink her eyes, has no pulse, and cannot feel the difference between hot and cold, the scientist is removed from the project. At the research institute, Clarke is killed and the space travel formula destroyed. Julie confesses that she is an alien from another planet that has already discovered the secret of mind travel; originally sent to kill Davidson, she failed because of her love for him. Following her confession, Julie is killed by her people and only her clothes remain. Davidson runs to the institute and is about to be killed by Miss Ballard, a secretary, when Lancaster saves him. Miss Ballard jumps out of a window, and like Julie, all that remains of her is her clothes. As Davidson and Lancaster walk into the street, they are surrounded by alien women with unblinking eyes.