TECHNOLOGY FOCUS - POLYMERS - Preparation (claimed): The hyperbranched polymer is obtained in one step by heating a solution containing cyanuric halide or a diaminoaryl compound, and an organic solvent at 60-150 degrees C, and adding diaminoaryl compound or cyanuric halide to the solution. Preferred Polymer: The repeating unit is of formula (III, IV or V). The polymer has triazine ring terminal(s) which is capped with alkyl group, aralkyl group, aryl group, alkylamino group, alkoxysilyl group containing alkylamino group, aralkylamino group, arylamino group, alkoxy group, aralkyloxy group, aryloxy group, or ester group. The polymer has a weight average molecular weight of 500-500000 and a refractive index at 550 nm of 1.7 or more, and does not have a sulfur atom in the molecule. Preferred Conditions: Cyanuric halide and diaminoaryl compound are reacted at -50 degrees C to 50 degrees C in an organic solvent, and then at 60-150 degrees C. The cyanuric halide compound and diaminoaryl compound are polymerized in presence of 0.05-500 equivalent organic monoamine with respect to the cyanuric halide compound. EXAMPLE - (In g) 9,9-bis(4-aminophenyl)fluorene (9.29) was added to a flask under air and dissolved in N,N-dimethylacetamide (DMAc) (80 mL). The mixture was heated at 100 degrees C with an oil bath. 2,4,6-Trichloro-1,3,5-triazine (3.69) dissolved in DMAc (20 mL) was added and polymerization was started. Aniline (3.34) was added 5 minutes later, the reaction mixture was stirred for 10 minutes, and polymerization was stopped. Potassium carbonate (15) dissolved in water (1000 mL) was added and reprecipitation was carried out after cooling to room temperature. The deposit was filtered, dissolved in tetrahydrofuran (50 mL), and reprecipitated in hexane (540 mL) and ethanol (60 mL). The obtained deposit was filtered and dried for 6 hours at 40 degrees C, to obtain a high-molecular compound (12.4) of formula (III). The compound had a weight average molecular weight of 9200 by polystyrene conversion, and a polydispersion degree of 2.33, as measured by gel permeation chromatography. Under air, the obtained high molecular compound (901) was added to a flask, and cyclohexanone (3.9950) was added as a solvent. Subsequently, 5 %mass cyclohexanone solution (0.0100) of Megaface R-30 (RTM: fluorine type surfactant) was added and stirred for 3 hours until the solution became uniform. The solute dissolved completely after stirring and the total solid content of the obtained polymer varnish was 10 %mass. A film of thickness 531.3 nm formed using the varnish had a refractive index of 1.7250 at 550 nm and 1.7025 at 633 nm.