Screening designs are attractive for assessing the relative impact of a large number of factors on a response of interest. Engineers prefer factors with three levels over two-level factors because having three levels allows for some assessment of curvature in the factor-response relationship. Yet, the most familiar screening designs limit each factor to only two levels. We propose a new class of designs that have three levels, allow for the estimation of quadratic effects, and have the property that the linear effect of every factor is independent of all second-order effects. We also provide an algorithm for design construction.