Structured illumination microscopy (SIM) breaks the optical diffraction limit by illuminating a sample with a series of line-patterned light. Recently, in order to alleviate the requirement of precise knowledge of illumination patterns, structured illumination microscopy techniques using speckle patterns have been proposed. However, these methods require stringent assumptions of the speckle statistics: for example, speckle patterns should be nearly incoherent or their temporal average should be roughly homogeneous. Here, we present a novel speckle illumination microscopy technique that overcomes the diffraction limit by exploiting the minimal requirement that is common for all the existing super-resolution microscopy, i.e. that the fluorophore locations do not vary during the acquisition time. Using numerical and real experiments, we demonstrate that the proposed method can improve the resolution up to threefold. Because our proposed method succeeds for standard fluorescence probes and experimental protocols, it can be applied in routine biological experiments.