We show that the integral of the first Pontrjagin class is given by an integer and it is identified with instanton number of the U(n) gauge theory on noncommutative R 4 . Here the dimension of the vector space V that appear in the ADHM construction is called Instanton number. The calculation is done in operator formalism and the first Pontrjagin class is defined by converge series. The origin of the instanton number is investigated closely, too. *

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We found an exact solution of elongated U(1) instanton on noncommutative R 4 for general instanton number k. The deformed ADHM equation was solved with general k and the gauge connection and the curvature were given explicitly. We also checked our solutions and evaluated the instanton charge by a numerical calculation.