The contour of constant area of error boundary is equal to contour of the probability density of the fix. On the other hand, radial error constructed by radius of max error is the easiest way in constructing and has more ever practical value. It is to say that the radial error is not theoretically good enough. We study that the error boundary of Running Fix by using max error parallelogram and max radial errors. We consider that the fix is obtained by two position lines from the same object by Running Fix method is equal to the fix by simultaneous observation by cross bearing from S_1 and S_2 which is advanced object S_1 existing in the error boundary of estimated position when ship's running course or distance is wrong. We constructed contours of constant probability density for Running Fix, and also, contours of radial error. So, we made a comparative study of the both contours. That is, 1. The best way of determining the fix by Running Fix method is to observe the bearing of the object at the close of ship's head line in the first observation, and to observe the bearing of the same object at the points to see it within 20°abaft the beam at the second observation. 2. The figure of contours of radial error is different from the figure of contours of constant probability density at the area that angle of cut is obtused. This fact is point out by the roughness of radial error, therefore, figures of these contours have become to contrary way. By the above contours, we think tha the error of Running Fix is made to clear.