Ultrasound elastography is the method to image the elasticity of compliant tissues due to a mechanical compression applied to it. In elastography, the local strain of explored tissue is estimated by analyzing the echo signals. This is accomplished by a sonographer who uses ultrasound transducer to apply pressure on the tissue area causing displacement of the tissue. A set of data is obtained before and after the compression. This stress along the axial direction not only causes deformation in that direction but it can also cause lateral deformation in the tissue. This relative deformation is later calculated using tracking algorithms. Finally, estimating the elasticity, images are formed. In this paper, we introduce a novel strain estimator. The proposed 1.5D strain estimator uses 1D windows for swift computations and searches the lateral direction for taking the non-axial movement into account. We have investigated the performance of our estimator using simulated and in-vivo data of breast tissue. The performance of our method is verified by comparing with different methods up to 16\% applied strain. The proposed estimator has exhibited a superior performance compared to the conventional methods. The image quality significantly improves, especially in the presence of higher applied strain, when the non-axial motion is significant.