The problem of neutral fermions subject to a pseudoscalar potential is investigated. Apart from the solutions for E = ±mc2, the problem is mapped into the Sturm-Liouville equation. The case of a singular trigonometric tangent potential (~tan.x) is exactly solved and the complete set of solutions is discussed in some detail. It is revealed that this intrinsically relativistic and true confining potential is able to localize fermions into a region of space arbitrarily small without the menace of particle-antiparticle production. © 2007 IOP Publishing Ltd.