This invention provides a rapidly solidified non-oriented electrical sheet having a high magnetic flux density and having a low iron loss. The invention also provides a method for manufacturing a non-oriented electrical sheet having a high magnetic flux density and a low iron loss, wherein, in solidifying a molten steel comprising predetermined constituents on the surface of a cooling body being moved and renewed to prepare a cast steel strip, one or at least two of REMs and Ca are incorporated in a total amount of 0.0020 to 0.01% in the molten steel and casting is carried out in a casting atmosphere of Ar, He or a mixed atmosphere composed of Ar and He.