The difficulty is first shown in the nonlinear interpolation of functions defined in a space of very many dimensions. There is a method using a sampling technique [J. ACM, Vol. 17, pp. 420–425, July 1970] that works fairly well in the regime ofk~10–20 (k=number of dimensions). The sampling errors, however, increase exponentially with increasingk, so that fork greater than the above values the computation is no more feasible. This is due to the subtraction between two large sums of about the same magnitude, each of which suffers stochastic fluctuations accompanying the samplings. To avoid this difficulty, a pairwise sampling method is devised where one draws two samples at a time when required, one from each of these two sums of terms. With the use of this technique, standard errors are reduced by orders of magnitude. Some details of algorithm are given together with typical computed examples.