The conventional iterative outlier detection procedures (CIODP), such as the Baarda-, Pope-, or t-testing procedure, based on the least-squares estimation (LSE) are used to detect the outliers in geodesy. Since the finite sample breakdown point (FSBP) of LSE is about 1/n, the FSBPs of the CIODP are also expected to be the same, about 1/n. In this paper, this problem is studied in view of the robust statistics for coordinate transformation with simulated data. Outliers have been examined in two groups: ''random'' and ''jointly influential.'' Random outliers are divided again into two subgroups: ''random scattered'' and ''adjacent.'' The single point displacements can be thought of as jointly influential outliers. These are modeled as the shifts along either the x- and y-axis or parallel to any given direction. In addition, each group is divided into two subgroups according to the magnitude of outliers: ''small'' and ''large.'' The FSBPs of either the Baarda-, Pope-, or t-testing procedure are the same and about 1/n. It means that only one outlier can be determined reliably by CIODP. However, the FSBP of the chi(2)-test is zero.