High resolution global irradiance time series are needed for accurate simulations of photovoltaic (PV) systems, since the typical volatile PV power output induced by fast irradiance changes cannot be simulated properly with commonly available hourly averages of global irradiance. We present a two-step algorithm that is capable of synthesizing one-minute global irradiance time series based on hourly averaged datasets. The algorithm is initialized by deriving characteristic transition probability matrices (TPM) for different weather conditions (cloudless, broken clouds and overcast) from a large number of high resolution measurements. Once initialized, the algorithm is location-independent and capable of synthesizing one-minute values based on hourly averaged global irradiance of any desired location. The one-minute time series are derived by discrete-time Markov chains based on a TPM that matches the weather condition of the input dataset. One-minute time series generated with the presented algorithm are compared with measured high resolution data and show a better agreement compared to two existing synthesizing algorithms in terms of temporal variability and characteristic frequency distributions of global irradiance and clearness index values. A comparison based on measurements performed in Lindenberg, Germany, and Carpentras, France, shows a reduction of the frequency distribution root mean square errors of more than 60% compared to the two existing synthesizing algorithms.