In this paper, a new 2-bit error correcting (DEC) linear code is presented as a modification of a corresponding 2-bit error correcting (DEC) BCH code. Compared to an unchanged BCH code in \(GF(2^m)\) with \(2\cdot m\) check bits and a code length of \(2^m-1\) , the number of data bits can be increased by at least \(m+1\) bits. The number of check bits only needs to be increased by 1. New columns and a single new row are added to the parity check matrix of the unchanged BCH code. The added columns are determined according to the columns of a parity check matrix of any 2-bit error correction code with only m check bits. The bits of the added row distinguish between the columns of the unchanged BCH code and the columns of the added columns. The proposed method is particularly interesting for longer code lengths. Decoding remains simple even with long code lengths, as the known algebraic methods for decoding BCH codes can be used for most of the bits. A small look-up table is only required for the relatively small number of bits added.