Let k be a field, \(A=k\Delta\) be the path algebra of a finite connected quiver \(\Delta\) without oriented cycles and A-mod the category of finite dimensional left A-modules. Let n be the number of vertices of \(\Delta\). A module Z in A-mod is called a Schur module if End Z\(=k\) and \(Ext^ 1_ A(Z,Z)=0\). The set of isoclasses of Schur modules carries the structure of a simplicial complex, where an i-simplex is an \((i+1)\) element set \(\{M_ 0,...,M_ i\}\) of Schur modules with \(Ext^ 1_ A(M_ j,M_ s)=0\) for \(0\leq j,s\leq i\). If A is representation-finite or tame, or \(n=2\), then all Schur modules are known. The author considers the case when A is wild and \(n=3\). The unknown Schur modules in this case are the DTr-sincere ones, that is, the Schur modules Z such that \((DTr)^ sZ\) is sincere for all integers s. The main theorem shows that, for a DTr-sincere Schur module Z from A-mod, there exists an integer r and a uniquely determined chain of Schur modules in A-mod \((DTr)^ rZ=Y_ m\to Y_{m-1}\to...\to Y_ 1\to Y_ 0,\) where \(Y_ 0\) is a regular Schur module over a quotient \(A'=A/<e>\) of A by the ideal \(<e>\) generated by a primitive idempotent e, the modules \(Y_ i\), \(1\leq i\leq m\), are DTr-sincere and \(Y_{i-1}\) is simple injective in the left perpendicular category \(^{\perp}Y_ i\) of \(Y_ i\). This gives an effective way of constructing all Schur modules in A-mod (up to DTr- translates) and all simplices of the simplicial complex of Schur modules in A-mod containing a given Schur module. The main tools used in the paper are the perpendicular categories of Schur modules and tilting theory.