  In this paper, we calculate the 2-local unstable homotopy groups of
indecomposable $\mathbf{A}_3^2$-complexes. The main technique used is analysing
the homotopy property of $J(X,A)$, defined by B. Gray for a CW-pair $(X,A)$,
which is homotopy equivalent to the homotopy fibre of the pinch map $X\cup
CA\rightarrow \Sigma A$.
