  Using the United Nations COMTRADE database \cite{comtrade} we construct the
Google matrix $G$ of multiproduct world trade between the UN countries and
analyze the properties of trade flows on this network for years 1962 - 2010.
This construction, based on Markov chains, treats all countries on equal
democratic grounds independently of their richness and at the same time it
considers the contributions of trade products proportionally to their trade
volume. We consider the trade with 61 products for up to 227 countries. The
obtained results show that the trade contribution of products is asymmetric:
some of them are export oriented while others are import oriented even if the
ranking by their trade volume is symmetric in respect to export and import
after averaging over all world countries. The construction of the Google matrix
allows to investigate the sensitivity of trade balance in respect to price
variations of products, e.g. petroleum and gas, taking into account the world
connectivity of trade links. The trade balance based on PageRank and CheiRank
probabilities highlights the leading role of China and other BRICS countries in
the world trade in recent years. We also show that the eigenstates of $G$ with
large eigenvalues select specific trade communities.
