This paper considers simultaneous modelling of seasonality, slowly changing un- conditional variance and conditional heteroskedasticity in high-frequency fiancial returns. A new approach, called a seasonal SEMIGARCH model, is proposed to perform this by introducing multiplicative seasonal and trend components into the GARCH model. A data-driven semiparametric algorithm is developed for estimat- ing the model. Asymptotic properties of the proposed estimators are investigated briefly. An approximate significance test of seasonality and the use of Monte Carlo confidence bounds for the trend are proposed. Practical performance of the pro- posal is investigated in detail using some German stock price returns. The approach proposed here provides a useful semiparametric extension of the GARCH model.