If $(M,g)$ is a pseudo-Riemannian $n$-dimensional manifold, then the tangent bundle $TM$ admits a pair of complementary $n$-dimensional distributions $V$ and $H$. The distribution $V$ is the vertical distribution given by spaces tangent to the fibres, while the horizontal distribution $H$ can be defined in a canonical way using the Christoffel symbols of the Levi-Civita connection of $g$. The author uses $g$ (on $V$) and a special deformation of $g$ (on $H$) to define families of metrics $G$ on $TM$ such that $V$ and $H$ are complementary orthogonal. The split $T(TM)=V\oplus H$ is exploited, once more, to define an almost complex structure $F$ on $TM$ such that the pairs $(G,F)$ are almost Hermitian structures. The author proves that these almost Hermitian structures are locally conformal almost Kählerian, and gives necessary and sufficient conditions for them to be almost Kähler. The paper then ends with a treatment of the case when $(M,g)$ is of constant curvature. In this case, sufficient conditions were given for $(G,F)$ to be locally conformal Kähler structures.