A patient is described who is affected by an inability to recall and use ‘arithmetical facts ’ of one-digit multiplications and divisions. This loss contrasts with the preservation of a wide set of complex notions that the patient exploits in order to overcome his deficit and get the right result. This observation helps in isolating and describing an important component of arithmetical long-term memory that is not overlearnt and the functioning of which is not automatic or mechanistic. An account of such a component is lacking in models of arithmetic currently referred to in cognitive neuropsychology. In a remediation study, performed over several weeks, the effect of training was selective for each single arithmetical fact: not even skills with multiplication complements (e.g. 6 × 3, 3 × 6) fully benefited from the rehabilitation of a specific fact. This suggests that the storage format of each fact is independent from that of other facts.