A New $N = 4$ Superconformal Algebra

It is shown that the previously known $N=3$ and $N=4$ superconformal algebras can be contracted consistently by singular scaling of some of the generators. For the later case, by a contraction which depends on the central term, we obtain a new $N=4$ superconformal algebra which contains an $SU(2)\times {U(1)}^4$ Kac-Moody subalgebra and has nonzero central extension.