The main purpose of this article was to identify whether an interpersonal motor co-ordination emerges between two participants when they intentionally tried to not co-ordinate their movements between each other. To do this we conjointly examined both the emergence of the motor co-ordination (collective properties) between the two participants, and the maintenance of the individual intrinsic motor properties present in the interpersonal co-ordination. Six pairs of participants performed three situations where they freely moved their right forearm with no instructions (nor restrictions) on frequency or relative phase. The goal of the first two situations was for participants to intentionally co-ordinate (P-on) or not co-ordinate (P-off) their movements between each other. In order to determine his/her individual motor properties, each participant performed this task alone, in a third condition. The cross-wavelet transform (CWT) revealed in the P-off condition the emergence of an unintended co-ordination in the frequency domain. Moreover, random distribution of the relative phase appeared, in this condition, whereas in the P-on condition, we observed a collective organization especially at a relative phase around 0°. Conjointly, the wavelet transform (WT) showed the presence of individual intrinsic motor properties (motor signature) in the three conditions. These results indicate that, when there was information sharing, participants could not avoid (unintentionally) coordinating with someone. This study suggests that, in daily life, interactions with other people lead the individual motor behavior to adapt unintended motor co-ordination.