Abstract: Two improved algorithms for non-orthogonal joint diagonalization free of degenerate solutions are presented to reduce the computational load of the original algorithm.On one hand,the determinant of the diagonalization matrix is directly expanded via its current updating column to reduce one matrix inverse operation.On the other hand,the other improved algorithm is developed by LU factorization of the column exchanged diagonalization matrix.As a result,the improved algorithms are computationally inexpensive since both of them reduce one matrix inverse operation in comparison with the original one.In the end,the computer simulation results show that two improved algorithms have a reduced computational load which is equal to 36.8% and 21.5% of that of the original one respectively when the number and dimension of the objective matrix are relatively large.