Determining the kinds of gamma-ray bursts (GRBs) has been of interest to astronomers for many years. We analysed 1599 GRBs from the Burst and Transient Source Experiment (BATSE) 4Br catalogue using t-mixture-model-based clustering on all nine observed parameters (T₅₀, T₉₀, F₁, F₂, F₃, F₄, P₆₄, P₂₅₆, and P₁₀₂₄) and found evidence of five types of GRBs. Our results further refine our earlier findings by providing groups that are more distinct. Using the classification scheme of past authors that employed duration, total fluence (F_t = F₁ + F₂ + F₃ + F₄), and spectrum [using Hardness Ratio H₃₂₁ = F₃/(F₁ + F₂)], our five groups are classified as long-intermediate–intermediate, short-faint-intermediate, short-faint-soft, long-bright-hard, and long-intermediate-hard. We also classify 374 GRBs in the BATSE catalogue that have incomplete information in some of the observed variables (mainly the four time integrated fluences F₁, F₂, F₃, and F₄) to the five groups obtained, using the 1599 GRBs having complete information in all the observed variables. Our classification scheme puts 138 GRBs in the first group, 52 GRBs in the second group, 33 GRBs in the third group, 127 GRBs in the fourth group, and 24 GRBs in the fifth group.