Supersaturated designs are useful in situations in which the number of active factors is very small compared to the total number of factors being considered. In this article, a new class of supersaturated designs is constructed using half fractions of Hadamard matrices. When a Hadamard matrix of order N is used, such a design can investigate up to N - 2 factors in N/2 runs. Results are given for N less-than-or-equal-to 60. Extension to larger N is straightforward. These designs are superior to other existing supersaturated designs and are easy to construct. An example with real data is used to illustrate the ideas.