We describe in this work a five-qubit quantum convolutional error correcting code and its implementation on a classical computer. The encoding and decoding circuits and an error correction procedure are presented. We will verify that if any X, Y, Z error or any product of them occurs on one or two qubit, this correction always allows to recover the useful information or to obtain a list of possible errors. The originality in this correction is the winning time obtained by measuring only the required syndromes, thus avoiding the decoherence phenomenon. Also, we give the average fidelity for double errors recovered as single errors having same syndrome.