In order to reduce mismatch error of a DAC used in a multibit delta-sigma some dynamic element matching (DEM) algorithms have been proposed before, from which Data-Weighted-Averaging (DWA) method is more hardware efficient and widely used. Unfortunately, DWA technique loses its functionalities for periodic signals which cannot be practically avoided. Many improvements have been suggested to minimize in band tone generated by DWA algorithm, but they cause limited performance compared with an ideal first order DEM. This paper presents a new modified DWA structure, which results in a completely first order mismatch noise shaping while solving in band tone problem. Simulations are presented for a 3rd-order lowpass delta sigma. However, its modified version can also be used in bandpass applications.