  Exploring topological phases in non-Hermitian systems has attracted
significant recent attention. One intriguing question is how topological edge
states compete with the non-Hermitian skin effect. Here, we report the
experimental observation of corner states in a two-dimensional non-reciprocal
rhombus honeycomb electric circuit. We construct non-reciprocal and
non-Hermitian circuits by introducing current-direction resolved capacitance
between two nodes depends on the current direction. Skin effect thus emerges
due to the non-reciprocity and prevails in dragging the corner state into the
bulk. The non-Bloch winding number defined in generalized Brillouin zone is
adopted to characterize the topological phase transition. Interestingly, we
find that the non-Bloch $Z_2$ Berry phase can serve as an invariant to describe
the non-Hermitian topology. By tuning the non-reciprocal parameter, we observe
unbalanced distribution of corner states emerging on two acute angles of the
rhombus lattice, with the localization length of the left corner state
increasing exponentially with the degree of non-reciprocity.
