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We present an explicit algorithm to compute a closed basis of the local dual space of I=(f"1,...,f"t) at a given isolated singular solution x@?=(x@?"1,...,x@?"s) when the Jacobian matrix J(x@?) has corank one. The algorithm is efficient both in time and memory use. Moreover, it can be modified to compute an approximate basis if the coefficients of f"1,...,f"t and x@? are only known with limited accuracy.