The decreasing order of stability of oxides of halogen is

In oxides of halogen, the bonds are mainly covalent due to small difference in electronegativity between the halogens and oxygen. The bond polarity, however, increases as we move from $F$ to $I$. The stability of oxides of iodine is greater than those of chlorine, while bromine oxides are the least stable. Iodine-oxygen bond is stable due to greater polarity of the bond, while the stability of the chlorine-oxygen bond is due to multiple bond formation involving $d$-orbitals of the chlorine atom. Bromine being in between lacks both these characteristics. Thus, the stability of oxides of halogens decreases in the following order $$ \mathrm{I}>\mathrm{Cl}>\mathrm{Br}>\mathrm{F} $$