The Clar structure of polybenzenoid hydrocarbons (PBHs) have attracted considerable interest of both theoretical and experimental chemists since it was proposed in the 1950s. However, it remains unclear whether the Clar structure could exist in inorganic PBHs, the boron nitride (BN) analogues where the alternate boron and nitrogen atoms are used to replace the carbon atoms of PBHs. Here, we carry out thorough density functional theory (DFT) calculations to probe the possibility of Clar structures in BN analogues of PBHs.