In this work we describe a technique developed to improve medium-term prediction methods of monthly smoothed sunspot numbers. Each month, the predictions are updated using the last available observations (see the monthly output in real time at http://sidc. oma. be/products/kalfil). The improvement of the predictions is provided by applying an adaptive Kalman filter to the medium-term predictions obtained by any other method, using the six-monthly mean values of sunspot numbers covering the six months between the last available value of the 13-month running mean (the starting point for the predictions) and the "current time" (i. e. now). Our technique provides an effective estimate of the sunspot index at the current time. This estimate becomes the new starting point for the updated prediction that is shifted six months ahead in comparison with the last available 13-month running mean, and it provides an increase of prediction accuracy. Our technique has been tested on three medium-term prediction methods that are currently in real-time operation: The McNish-Lincoln method (NGDC), the standard method (SIDC), and the combined method (SIDC). With our technique, the prediction accuracy for the McNish-Lincoln method is increased by 17 - 30%, for the standard method by 5 - 21% and for the combined method by 6 - 57%.