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This paper proposes the cross-parity check as a method for an on-line detection of multiple bit-errors in storage elements of microprocessors like registers or register files. Transient or 'soft' errors caused by radiation or electromagnetic influences are the focus of this work. Especially for register files or register groups, an easy implementable error correction method is proposed, which can be performed by software routines or additional hardware. The method is based on the logical interpretation of cross-parity vectors.