Inversion over finite fields is the most costly basic operation for diverse cryptographic applications, such as elliptic curve cryptography and others. The Itoh-Tsujii algorithm (ITA) provides high performance implementations for the inversion operation in standard bases through diverse versions like squarer-ITA, parallel squarer-ITA or quad-ITA. A new modification of the ITA algorithm allows the inversion over finite fields in a minimal number of clock cycles. The proposed implementations complete the inversion over GF(2233) or GF(2409) from only 10 clock cycles.