  Highest weight modules of the double affine Lie algebra
$\widehat{\widehat{\mathfrak{sl}}}_{2}$ are studied under a new triangular
decomposition. Singular vectors of Verma modules are determined using a similar
condition with horizontal affine Lie subalgebras, and highest weight modules
are described under the condition that $c_1>0$ and $c_2=0$.
