The authors present a sparsity-based algorithm, basic thresholding classifier (BTC), for classification applications which is capable of identifying test samples extremely rapidly and performing high classification accuracy. They introduce a sufficient identification condition (SIC) under which BTC can identify any test sample in the range space of a given dictionary. By using SIC, they develop a procedure which provides a guidance for the selection of threshold parameter. By exploiting rapid classification capability, they propose a fusion scheme in which individual BTC classifiers are combined to produce better classification results especially when very small number of features is used. Finally, they propose an efficient validation technique to reject invalid test samples. Numerical results in face identification domain show that BTC is a tempting alternative to sparsity-based classification algorithms such as greedy orthogonal matching pursuit and l(1)-minimisation.