The use of a ferromagnetic transformer coupled to a SQUID, as previously described, per mits to measure very low currents. A low loss ceramic core for the transformer has yielded to further increase in the sensitivity of about two orders of magnitude in a narrow-band around a fixed frequen cy. At present the achieved sensitivity of about 8 x 10-1* pA in 1 Hz bandwidth at 150 Hz. The use of a superconducting magnetometer as a high sensitivity current detector has been propo sed by some authors a few years ago /1,2,3/. More recently, by coupling a transformer with a ferroma gnetic core to a rf SQUID /4/, we have enhanced the overall current*sensitivity up to very interesting figures /5/. Due to the particular ferromagnetic material employed /6/ the useful bandwidth of the device was constrained between dc and a corner fre quency dictated by the strong frequency dependence of the relative permeability of the used core. In order to enhance the current sensitivity at a fixed frequency we inserted a tuning capacitor in the input circuit. However, due to the high value of the electrical conductivity of the core a large amount of eddy-current losses was present, limiting the Q of the urned circuit to not interesting va lues. This drawback has been overcome by means of a suitable choice of a ceramic core for. the trans former. We have tested a few commercially available ferrites in order to select those which preserve an acceptable value of the relative permeability at li quid helium temperature. The chosen material has been used to make up a superconducting transformer coupled to the SUID as shown in figure 1. The cur rent I (v) is supplied by a current generator I to the input circuit which consists of a capacitance C paralleled to the primary L (N turns) of the transformer. The secondary winding L (N turns) is connected with the inductance L to obtain as usual a flux transformer. All winding are made of super conducting wire. M™ = K_p/L L is the mutual in ductance between L and L , while M = K/L L is the mutual inductance between L and the inductance of the SQUID, L.