Suppose $(M,J,g,\Omega)$ is a Calabi–Yau $m$-fold and $(L,E)$ is an immersed Lagrangian brane in $M$ with only transverse self-intersections. If $b_{m-2}(L)=0$ and $L$ has no self-intersection points $p$ with $\mu_{L^{+},L^{-}}(p)=2$ or $m-2,$ where $L_{\pm}$ are the local sheets of $L$ at $p,$ then $(L,E)$ has $HF^{*}$ unobstructed.