This paper proposes a new variant of NTRU with a slightly different critical formulation. The significance of this new variant is that it requires an additional private key to provide a tighter scheme. Because of these changes, modified key generation, encryption and decryption algorithms have been developed accordingly. The new variant is analyzed and tested against several well-known attacks, namely the alternate private key attack, brute force attack, meet-in-the-middle attack, multiple transmission attacks and lattice attack. Security properties related to these attacks have been established and explored to ensure the new variant is secure against the said attacks. Several examples are provided to illustrate the ideas.