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 Direct sum for basic cohomology of codimension four taut Riemannian foliation Bull. Korean Math. Soc.Published online July 17, 2020 Jiuru Zhou Yangzhou University Abstract : We discuss the decomposition of degree two basic cohomology for codimension four taut Riemannian foliation according to the holonomy invariant transversal almost complex structure $J$, and show that $J$ is $C^{\infty}$ pure and full. In addition, we obtain an estimate of the dimension of basic $J$-anti-invariant subgroup. These are the foliated version for the corresponding results of T. Draghici et al. (Int. Math. Res. Not. IMRN 1:1–17, 2010). Keywords : Riemannian foliation, basic cohomology, transversal almost complex structure MSC numbers : 53D10; 53C25; 53D35 Full-Text :