We present a parameterized algorithm that, given a graph G on n vertices and an integer parameter k, decides whether G has an independent set of size at most k in time O(2^{2.1152k+0.1028n}). When k is less than or equal to 0.0607n, the running time of our algorithm is bounded by O(2^{n/4}), improving the very recent O(2^{0.288n}) time algorithm by Fomin, Grandoni, and Kratsch.