High-order sequential simulation methods have been developped as an alternative to existing frameworks to facilitate the modelling of spatial complexity of non-Gaussian variables of interest. The high-order simulation approaches address the modelling of curvilinear features and spatial connectivity of extreme values that are common in mineral deposits, petroleum reservoirs, water aquifers and other geological phenomena. This paper presents a new high-order simulation method that generates realizations directly at the block support, conditioned to the available data at point support scale. Under the context of sequential high-order simulation, the method estimates, at each block location, the cross-support joint probability density function using Legendre-like splines as the set of basis functions. The proposed method adds previously simulated blocks to the set of conditioning data, which initially contains the available data at point support. A spatial template is defined by the configuration of the block to be simulated and related conditioning values in both support scales and is used to infer additional high-order statistics from a training image. Through testing the proposed method with an exhaustive dataset, it is shown that simulated realizations reproduce major structures and high-order relations of data. The practical intricacies of the proposed method are demonstrated in an application at a gold deposit.