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We present a new method to resolve the 180° ambiguity for solar vector magnetogram measurements. The basic assumption is that the magnetic shear angle (δθ), which is defined as the difference between the azimuth components of observed and potential fields, approximately follows a normal distribution. The new method is composed of three steps. First, we apply the potential field method to determine the azimuthal components of the observed magnetic fields. Second, we resolve the ambiguity with a new criterion: −90°+δθmpleδθle 90° + δθmp, where δθmp is the most probable value of magnetic shear angle from its number distribution. Finally, to remove some localized field discontinuities, we use the criterion Bt⋅Bmtge 0, where Bt and Bmt are an observed transverse field and its mean value for a small surrounding region, respectively. For an illustration, we have applied the new ambiguity removal method (Uniform Shear Method) to a vector magnetogram which covers a highly sheared region near the polarity inversion line of NOAA AR 0039. As a result, we have found that the new ambiguity solution was successful and removed spatial discontinuities in the transverse vector fields produced in the magnetogram by the potential field method. It is also found that our solution to the ambiguity gives nearly the same results, for highly sheared vector magnetograms and vertical current density distributions, of NOAA AR 5747 and AR 6233 as those of other methods. The validity of the basic assumption for an approximate normal distribution is demonstrated by the number distributions of magnetic shear angle for the three active regions under consideration.