A razor having a pivotable blade unit which is biased into a rest position by a biasing plunger. The razor includes a stabilizing bore in which a penetrating portion of the biasing plunger is configured to reciprocate. The largest cross-section of the penetrating portion has a shape which differs from the shape of the smallest cross-section of the stabilizing bore in order to lower the contact area between the penetrating portion of the biasing plunger and the stabilizing bore.