Code Division Multiple Access (CDMA) is a widely used multiple access method in a lot of nowadays vital applications. The systems that are designed based on CDMA are suffering from multiple access interference (MAI) problem. A lot of CDMA detectors are designed to overcome the (MAI) problem. But as the capability of CDMA detector in (MAI) cancellation increases, the complexity of the detector increases too. This paper gives a proposal of a new linear CDMA detector that has the same multiple access interference (MAI) cancellation capability as CDMA decorrelator detector. The structure complexity of this new proposed detector is as simple as the matched filter detector structure. Solving the (MAI) problem in CDMA system with simple detector structure at the receiver helps on increasing the CDMA system capacity. The new proposed detector operation is based on the symmetry property of CDMA signatures' codes cross-correlation matrix.