Cokriging allows predicting variables from sampling information (e.g. boreholes and blast holes), taking into account their cross-correlation structures. When the bi-variate relations among the variables are non-linear and complex, cokriging results may suffer from reproducing the complexities of interest. Another property of this linear geostatistical algorithm is the smoothing effect in the estimated block model, in which it over and underestimates the original distribution of the variables. To come up with those difficulties, this paper proposes an innovative algorithm to integrate the cokriging approach with a factor-based methodology entitled "projection pursuit multivariate transform" to first reproduce the complexity among the variables and, second to manage the smoothing effect in traditional cokriging algorithms. To do so, six cross-correlated variables obtained from a blast hole campaign belonging to a Nickle-Laterite deposit are presented and tested with the algorithm proposed. The results indicated that this algorithm is dramatically capable of alleviating the smoothing effect while the complexity in cross-correlation characteristics among the variables can be preserved.