In finite population sampling it is common to use information from one or several auxiliary variables through indirect estimators, such as ratio or product estimators. We propose an alternative estimator to the generalized multivariate estimator for cases where several auxiliary variables correlate either positively or negatively with the main variable. This new almost unbiased estimator based on the jackknife technique is always more precise than either the simple expansion estimator (the sample mean) or than the ratio, product, or ratio - product estimators built using any of the available auxiliary variables. ; SeriesInformation ; Statistica; Vol 55, No 2 (1995)