NOVELTY - Preparing a benzoxazole-based polymer (I) involves thermal rearrangement of poly(hydroxyamide) (II).    USE - For preparing benzoxazole-based polymer useful in making gas separation membrane for gas pair of hydrogen/methane, hydrogen/carbon dioxide, hydrogen/nitrogen, helium/nitrogen, oxygen/nitrogen, carbon dioxide/nitrogen, and carbon dioxide/methane (claimed).    ADVANTAGE - The process is simple, produces polybenzoxazole at low temperatures. The polybenzoxazole exhibits superior mechanical and morphological properties and has well-connected microcavities, thus showing excellent permeability and selectivity for various types of gases. The gas separation membrane has a tensile strength of 85-90 MPa and an elongation of 5-10%; has well-connected microcavities and exhibits a superior fractional free volume, allowing gases to smoothly pass though the microcavities (good permeability); has a low d-spacing, thus exhibiting increased permeability and selectivity for small gases.    DETAILED DESCRIPTION - Preparing a benzoxazole-based polymer of formula (I) involves thermal rearrangement of poly(hydroxyamide) of formula (II).    Ar=bivalent 5-24C arylene, bivalent 5-24C heterocyclic ring, (both optionally substituted by at least one 1-10C alkyl, 1-10C alkoxy, 1-10C haloalkyl or 1-10C haloalkoxy);    p and q=1-10;    Q=O, S, C(=O), CH(OH), S(O)2, Si(CH3)2, (CH2)p, (CF2)q, C(CH3)2, C(CF3)2, C(=O)NH, C(CH3)(CF3), 1-6C alkyl-substituted phenyl or 1-6C haloalkyl-substituted phenyl (where the Q is linked to opposite both phenyl rings in the position of m-m, m-p, p-m or p-p);    n=20-200.    At least two of Ar are fused together to form a condensation ring, or covalently bonded to each other via a functional group selected from O, S, C(=O), CH(OH), S(O)2, Si(CH3)2, (CH2)p, (CF2)q, C(CH3)2, C(CF3)2 or C(=O)NH. INDEPENDENT CLAIMS are included for the following:    (1) new intermediate of poly(hydroxyamide) of formula (II);    (2) new polybenzoxazole (TR- beta -PBO) of formula (III) having a glass transition temperature (Tg) of 377 degrees C; and    (3) a gas separation membrane comprising the polybenzoxazole (III).