We introduce a two-parameter deformation of 2x2 matrices without imposing any condition on the matrices and give the universal R-matrix of the nonstandard quantum group which satisfies the quantum Yang-Baxter relation. Although in the standard two-parameter deformation the quantum determinant is not central, in the nonstandard case it is central. We note that the quantum group thus obtained is related to the quantum supergroup GL(p,q)(1\1) by a transformation. (C) 1999 American Institute of Physics. [S0022-2488(99)03806-2].