Abstract
We are now looking for the Painleve trascendents ,especially with any values of parameters,for which the monodromy data of the associated linear equation (we call the linear monodromy) can be explicitly calculated.The Pioneer of this work is A.V.Kitaev,who found the symmetric solution of the Painleve II equation with any value of parameter and calculated the linear monodromy(1991). R.Fuchs calculated the linear monodromy for the so called Picard's solution which satisfies the Painleve VI equation with special values of parameters:a=b=c=0,d=1/2(1911). We have found 12 solutions for the Painleve VI equation with any values of parameters,which are meromorphic at a fixed singularity. We show that these are invariant under the actions of the Backlund transformation group and the linear monodromy can be explicitly calculated.