We describe a simple algorithm that runs in time and learns an unknown n-dimensional -margin halfspace to accuracy in theppresence of malicious noise, when the noise rate is allowed to be as high as Previous efficient algorithms could only learn to accuracy in the presence of malicious noise of rate at mostOur algorithm does not work by optimizing a convex loss function. We show that no algorithm for learning -margin halfspaces that minimizes a convex proxy for misclassification error can tolerate malicious noise at a rate greater than this may partially explain why previous algorithms could not achieve the higher noise tolerance of our new algorithm.