  The linkage construction and its generalization is one of the most powerful
constructions for constant dimension code, accounting for approximately 50\% of
all the listed parameters. We show how to improve the linkage construction of
subspace codes by two parallel versions of the linkage construction. This proof
allows us to attain codes of larger size for a given minimum distance, which
exceeds the latest improvements on the linkage construction
\cite{combining2019Antonio} in the cases $A_q(13,4,4),A_q(17,4,4),
A_q(19,6,6)$.
