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Let $f\colon M^{2n}\to\mathbb{R}^{2n+4}$ be an isometric immersion of aKaehler manifold of complex dimension $n\geq 5$ into Euclidean space withcomplex rank at least $5$ everywhere. Our main result is that, along eachconnected component of an open dense subset of $M^{2n}$, either $f$ isholomorphic in $\mathbb{R}^{2n+4}\cong\mathbb{C}^{n+2}$ or it is in a uniqueway a composition $f=F\circ h$ of isometric immersions. In the latter case, wehave that $h\colon M^{2n}\to N^{2n+2}$ is holomorphic and $F\colonN^{2n+2}\to\mathbb{R}^{2n+4}$ belongs to the class, by now quite wellunderstood, of non-holomorphic Kaehler submanifold in codimension two.Moreover, the submanifold $F$ is minimal if and only if $f$ is minimal.

Real Kaehler submanifolds in codimension up to four