The method of continued fractions recently proposed by the authors is generalized to an off-shell t-matrix calculation for any nonlocal nonsymmetric interaction. The efficiency of the method is demonstrated for some examples in nuclear physics. The method is not only very efficient, but yields very accurate results when it is combined with the Romberg extrapolation method. A new separable approximation of a potential and the off-shell t matrix is proposed in connection with the method of continued fractions.