  We apply the FLAME methodology to derive algorithms hand in hand with their
proofs of correctness for the computation of the $ L T L^T $ decomposition
(with and without pivoting) of a skew-symmetric matrix. The approach yields
known as well as new algorithms, presented using the FLAME notation. A number
of BLAS-like primitives are exposed at the core of blocked algorithms that can
attain high performance. The insights can be easily extended to yield
algorithms for computing the $ L T L^T $ decomposition of a symmetric matrix.
