This paper applies the Johansen Cointegration procedure to test the law of one price (LOOP) for twelve international markets of paintings using semi-annual data for the period 1985-2007. Cointegration test is performed in a pairwise arrangement. Price index for each market is estimated using the repeat sales method. The order of integration of each price series was determined using the augmented Dickey-Fuller and the DF-GLS tests. The results show that only five price index series were I(1). The Johansen bivariate test supports the validity of the LOOP hypothesis only three pairwise systems out of the 66 systems, suggesting weak relationships among international art market.