  The holonomy algebra of a pseudo-hyper-K\"ahlerian manifold of signature
$(4,4n+4)$ is a subalgebra of $\sp(1,n+1)$. Possible holonomy algebras of these
manifolds are classified. Using this, a new proof of the classification of
simply connected pseudo-hyper-K\"ahlerian symmetric spaces of index 4 is
obtained.
