Internal perturbation is added to the TTM cryptosystem, and its new variant is constructed. Using small instances of the variant, the security of the new variant is investigated against minrank attack and linearization equation attack. The necessary condition is given, under which there do not exist linear equations in the variant of the TTM cryptosystem. Computer experiments indicate that there almost do not exist linear equations in the new variant. A specific instance is proposed for practical implementation, and its performance and security are estimated.