Multiferroics are promising for sensor and memory applications, but despite all efforts invested in their research no single-phase material displaying both ferroelectricity and large magnetization at room-temperature has hitherto been reported. This situation has substantially been improved in the novel relaxor ferroelectric single-phase (BiFe0.9Co0.1O3)(0.4)-(Bi1/2K1/2TiO3)(0.6), where polar nanoregions (PNR) transform into static-PNR as evidenced by piezoresponse force microscopy (PFM) and simultaneously enable congruent multiferroic clusters (MFC) to emerge from inherent strongly magnetic Bi(Fe,Co)O-3 rich regions as verified by magnetic force microscopy (MFM) and secondary ion mass spectrometry. The material's exceptionally large Neel temperature T-N = 670 +/- 10 K, as found by neutron diffraction, is proposed to be a consequence of ferrimagnetic order in MFC. On these MFC, exceptionally large direct and converse magnetoelectric (ME) coupling coefficients, approximate to 1.0 x 10(-5) s m(-1) at room-temperature, are measured by PFM and MFM, respectively. It is expected that the non-ergodic relaxor properties which are governed by the Bi1/2K1/2TiO3 component to play a vital role in the strong ME coupling, by providing an electrically and mechanically flexible environment to MFC. This new class of non-ergodic relaxor multiferroics bears great potential for applications. Especially the prospect of a ME nanodot storage device seems appealing.