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A study of certain symplectic $4$-orbifolds with vanishing canonical class isinitiated. We show that for any such symplectic $4$-orbifold $X$, there is acanonically constructed symplectic $4$-orbifold $Y$, together with a cyclicorbifold covering $Y\rightarrow X$, such that $Y$ has at most isolated Du Valsingularities and a trivial orbifold canonical line bundle. The minimalresolution of $Y$, to be denoted by $\tilde{Y}$, is a symplectic Calabi-Yau$4$-manifold endowed with a natural symplectic finite cyclic action, extendingthe deck transformations of the orbifold covering $Y\rightarrow X$.Furthermore, we show that when $b_1(X)>0$, $\tilde{Y}$ is a $T^2$-bundle over$T^2$ with symplectic fibers, and when $b_1(X)=0$, $\tilde{Y}$ is either anintegral homology $K3$ surface or a rational homology $T^4$; in the lattercase, the singular set of $X$ is completely classified. To further investigatethe topology of $X$, we introduce a general successive symplectic blowing-downprocedure, which may be of independent interest. Under suitable assumptions,the procedure allows us to successively blow down a given symplectic rational$4$-manifold to $CP^2$, during which process we can canonically transform agiven configuration of symplectic surfaces to a "symplectic arrangement" ofpseudoholomorphic curves in $CP^2$. The procedure is reversible; by a sequenceof successive blowing-ups in the reversing order, one can recover the originalconfiguration of symplectic surfaces up to a smooth isotopy.

On a class of symplectic $4$-orbifolds with vanishing canonical class