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For enhancing the performance of the characteristic-based method, the multidimensional characteristics of incompressible flows are applied for developing a novel efficient bicharacteristic-based method. The multidimensionality of information propagation is embedded in the convective flux computation by the directional derivatives along the bicharacteristics in conjunction with the cross derivative. The well-known benchmark problems (i.e. the cross flow around a circular cylinder, the lid-driven cavity flow, and the flow around a sphere) are solved to validate the proposed scheme in the presence of strong multidimensional interaction of separated vortical flow. The results represent significant consensus with the benchmark solutions. Furthermore, the proposed scheme results in significantly faster convergence and higher resolution in comparison with the characteristic-based method.