(HC-FCM) is a useful tool for dealing with collaborative clustering problems where a pattern-set is described in some different feature spaces independently and thus results in different data sets. By means of FCM, clustering may be carried on these different data sets and thus result in different partition matrices. For one of these data sets, how to take means of the clustering information of the other data sets to help its own clustering and thus to give a reasonable collaborative clustering result is a meaningful topic and becomes the aim of HC-FCM. Because of potential security and privacy restrictions, the clustering information can be provided only by partition matrices instead of the data sets themselves. This confines the manner of using the clustering information. In the original frame of HC-FCM given by W.Pedrycz, the partition matrices are directly introduced to the clustering algorithm without any preprocessing. In this paper, we will show the necessity of the preprocessing on the partition matrices and present an available method for the preprocessing. Some experiments are given to show the performance of the proposed method for preprocessing. With the work of this paper, the Horizontal Collaboration Fuzzy C-Means will be well carried on.