Magnetic materials are classed as 'soft' if they have a low coercivity (the critical field strength Hc required to flip the direction of magnetization).Soft magnetic materials are a central component of electromagnetic devices such as step motors, magnetic sensors, transformers and magnetic recording heads. Miniaturization of these devices requires materials that can develop higher saturation flux density, Bs, so that the necessary flux densities can be preserved on reducing device dimensions, while simultaneously achieving a low coercivity. Common high-Bs soft magnetic films currently in use are electroplated CoFe-based alloys [1-4], electroplated CoNiFe alloys [5-7] and sputtered Fe-based nanocrystalline [8-11] and FeN films [12-14]. Sputtering is not suitable, however, for fabricating the thick films needed in some applications, for which electrochemical methods are preferred. Here we report the electrochemical preparation of a CoNiFe film with a very high value of Bs (2.0-2.1 T) and a low coercivity. The favourable properties are achieved by avoiding the need for organic additives in the deposition process, which are typically used to reduce internal stresses. Our films also undergo very small magnetostriction, which is essential to ensure that they are not stressed when an external magnetic field is applied (or conversely, that external stresses do not disrupt the magnetic properties). Our material should find applications in miniaturization of electromechanical devices and in high-density magnetic data storage.