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Self-shrinking generators were introduced in 1994 and a modified self-shrinking generator was presented 2010.They employ a linear feedback shift register as the underlying sequence generator.In this article, a new self-shrinking generator is proposed that provides randomness similar to current self-shrinking generators but increases the security using an underlying non-linear feedback shift register.A generalization of the shrinking employed in previous generators is also given.It is shown both theoretically and experimentally using the NIST test suite that the proposed generator is more secure than current generators.