The paper presents a new iterative array, which performs the triangularisation of a dense matrix, using the Givens rotation algorithm. Two slightly different arrays are presented: the first performs the factorisation of a single matrix; the second performs the recursive triangularisation. Partitioning of the first structure is also considered, in order to cope with matrices larger than the array. The implementation of the cell in the array is based on on-line arithmetic, which allows us to obtain high performances. Furthermore, the cell implementation requires only three types of arithmetic units (multiplication/addition, square root, division) and shift registers for data buffering and for generating the timing signals.